## Justin P. Haldar: Publications

### Preprints

• T. H. Kim, P. Garg, J. P. Haldar.
LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive Reconstruction in k-Space.
arXiv:1904.09390

Purpose To propose and evaluate a new MRI reconstruction method named LORAKI that trains an autocalibrated scan-specific recurrent neural network (RNN) to recover missing k-space data.

Methods Methods like GRAPPA, SPIRiT, and AC-LORAKS assume that k-space data has shift-invariant autoregressive structure, and that the scan-specific autoregression relationships needed to recover missing samples can be learned from fully-sampled autocalibration (ACS) data. Recently, the structure of the linear GRAPPA method has been translated into a nonlinear deep learning method named RAKI. RAKI uses ACS data to train an artificial neural network to interpolate missing k-space samples, and often outperforms GRAPPA. In this work, we apply a similar principle to translate the linear AC-LORAKS method (simultaneously incorporating support, phase, and parallel imaging constraints) into a nonlinear deep learning method named LORAKI.
Since AC-LORAKS is iterative and convolutional, LORAKI takes the form of a convolutional RNN. This new architecture admits a wide range of sampling patterns, and even calibrationless patterns are possible if synthetic ACS data is generated.
The performance of LORAKI was evaluated with retrospectively undersampled brain datasets, with comparisons against other related reconstruction methods

Results Results suggest that LORAKI can provide improved reconstruction compared to other scan-specific autocalibrated reconstruction methods like GRAPPA, RAKI, and AC-LORAKS.

ConclusionLORAKI offers a new deep-learning approach to MRI reconstruction based on RNNs in k-space, and enables improved image quality and enhanced sampling flexibility.

• J. P. Haldar, K. Setsompop.
Linear Predictability in MRI Reconstruction: Leveraging Shift-Invariant Fourier Structure for Faster and Better Imaging.
arXiv:1903.03141.

Over the past several decades, many different types of computational imaging approaches have been proposed for improving MRI. In this paper, we provide an overview of methods that assume that MRI Fourier data is linearly predictable. Linear prediction is well known in signal processing and may be most recognizable for its usefulness in speech processing and spectrum estimation applications. In MRI, linear predictability implies that data can be sampled below the conventional Nyquist rate, since unmeasured data may be imputed as a shift-invariant linear combination of measured samples. Linear predictive methods include some of the earliest methods in the computational MRI reconstruction field, some of the most widely utilized computational MRI methods in modern clinical practice, and some of the most flexible and versatile modern computational imaging approaches that are enabling unprecedented new styles of data acquisition. In addition, the concept of linear predictability can be used to unify a number of more classical MRI reconstruction constraints, but without needing to make the strong assumptions of classical constrained reconstruction methods.

• D. Kim, J. L. Wisnowski, C. T. Nguyen, J. P. Haldar.
Multidimensional Correlation Spectroscopic Imaging of Exponential Decays: From Theoretical Principles to In Vivo Human Applications.
arXiv:1806.05752.

Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by the fact that one-dimensional multiexponential modeling is an ill-posed inverse problem with substantial ambiguities. In this paper, we present an overview of a recent multidimensional correlation spectroscopic imaging approach to this problem. This approach helps to alleviate ill-posedness by leveraging multidimensional contrast encoding (e.g., 2D diffusion-relaxation encoding or 2D relaxation-relaxation encoding) combined with a regularized spatial-spectral estimation procedure. Theoretical calculations, simulations, and experimental results are used to illustrate the benefits of this approach relative to classical methods. In addition, we demonstrate an initial proof-of-principle application of this kind of approach to in vivo human MRI experiments.

• R. Xu, M. Soltanolkotabi, J. P. Haldar, W. Unglaub, J. Zusman, A. F. J. Levi, R. M. Leahy.
Accelerated Wirtinger Flow: A fast algorithm for ptychography.
arXiv:1806.05546.

This paper presents a new algorithm, Accelerated Wirtinger Flow (AWF), for ptychographic image reconstruction from phaseless diffraction pattern measurements. AWF is based on combining Nesterov's acceleration approach with Wirtinger gradient descent. Theoretical results enable prespecification of all AWF algorithm parameters, with no need for computationally-expensive line searches and no need for manual parameter tuning. AWF is evaluated in the context of simulated X-ray ptychography, where we demonstrate fast convergence and low per-iteration computational complexity. We also show examples where AWF reaches higher image quality with less computation than classical algorithms. AWF is also shown to have robustness to noise and probe misalignment.

### Technical Reports

• T. H. Kim, J. P. Haldar.
LORAKS Software Version 2.0: Faster Implementation and Enhanced Capabilities.
University of Southern California, Los Angeles, CA, Technical Report USC-SIPI-443, May 2018.

Over the past several years, our research group has been developing a novel structured low-rank matrix modeling framework for magnetic resonance (MR) image reconstruction that we call LORAKS (LOw-RAnk modeling of local K-Space neighborhoods). In the spirit of reproducible research, we had previously released a public open-source software implementation of LORAKS-based image reconstruction in 2014. In the present technical report (and supplementary material available for download at http://mr.usc.edu/download/LORAKS2/), we describe an updated public open-source software release that provides access to many of the new developments we’ve made since 2014, including substantially-faster algorithms and a variety of new formulations of the inverse problem.

• J. P. Haldar.
Low-Rank Modeling of Local k-Space Neighborhoods (LORAKS): Implementation and Examples for Reproducible Research.
University of Southern California, Los Angeles, CA, Technical Report USC-SIPI-414, April 2014.
[toggle abstract] [link] [related software (outdated, see new version above)]

Our recent work has introduced a new signal processing framework that enables the recovery of magnetic resonance (MR) images from undersampled and/or noisy Fourier data, based on the assumptions that the true image has smooth phase and/or limited spatial support. This framework, named LORAKS, relies on embedding the Fourier data from such images into high-dimensional Hankel-like matrices, which we showed would have approximately low rank when the phase/support assumptions were satisfied. The fact that these matrices have low rank implies that they have relatively few degrees of freedom relative to their number of entries, and hence can potentially be recovered from subsampled data. In contrast to conventional reconstruction methods that rely on assumptions of smooth image phase and/or limited spatial support, LORAKS does not place strict requirements on the sampling scheme used for data acquisition, and high-quality reconstructions can be obtained from both highly-structured and highly-unstructured Fourier sampling schemes. In contrast to other recent MR image reconstruction methods based on low-rank modeling, LORAKS can be used with relatively low-dimensional single-channel, single-contrast, single-timepoint MR imaging data. We have also previously demonstrated that LORAKS has distinct features and advantages relative to sparsity-based MR image reconstruction methods (which have been receiving substantial attention over the past several years), which suggests that phase and support constraints can be used in combination with sparsity constraints for even better performance.
In the spirit of reproducible research, this technical report (and corresponding supplementary material available for download at http://mr.usc.edu/download/LORAKS/) provides a MATLAB implementation of a LORAKS-based reconstruction algorithm proposed in our previous work, and presents several application examples that are not found in the existing literature (including an example outside the context of MR imaging).

### Journal Publications

#### 2019

1. J. P. Haldar, D. Kim.
OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI.
IEEE Transactions on Medical Imaging 2019. In Press.
PubMed Central ID: In Process.

This paper introduces a new estimation-theoretic framework for experiment design in the context of MR image reconstruction under sparsity constraints. The new framework is called OEDIPUS (Oracle-based Experiment Design for Imaging Parsimoniously Under Sparsity constraints), and is based on combining the constrained Cramer-Rao bound with classical experiment design techniques. Compared to popular random sampling approaches, OEDIPUS is fully deterministic and automatically tailors the sampling pattern to the specific imaging context of interest (i.e., accounting for coil geometry, anatomy, image constrast, etc.). OEDIPUS-based experiment designs are evaluated using retrospectively subsampled in vivo MRI data in several different contexts. Results demonstrate that OEDIPUS-based experiment designs perform favorably in comparison to conventional MRI sampling approaches.

2. T. H. Kim, B. Bilgic, D. Polak, K. Setsompop, J. P. Haldar.
Wave-LORAKS: Combining Wave Encoding with Structured Low-Rank Matrix Modeling for More Highly Accelerated 3D Imaging.
Magnetic Resonance in Medicine 81:1620-1633, 2019.
PubMed Central ID: In Process.

Purpose Wave-CAIPI is a novel acquisition approach that enables highly accelerated 3D imaging. This paper investigates the combination of Wave-CAIPI with LORAKS-based reconstruction (Wave-LORAKS) to enable even further acceleration.

Methods LORAKS is a constrained image reconstruction framework that can impose spatial support, smooth phase, sparsity, and/or parallel imaging constraints. LORAKS requires minimal prior information, and instead uses the low-rank subspace structure of the raw data to automatically learn which constraints to impose and how to impose them. Previous LORAKS implementations addressed 2D image reconstruction problems. In this work, several recent advances in structured low-rank matrix recovery were combined to enable large-scale 3D Wave-LORAKS reconstruction with improved quality and computational efficiency. Wave-LORAKS was investigated by retrospective subsampling of two fully sampled Wave-encoded 3D MPRAGE datasets, and comparisons were made against existing Wave reconstruction approaches.

Results Results show that Wave-LORAKS can yield higher reconstruction quality with 16x-accelerated data than is obtained by taditional Wave-CAIPI with 9x-accelerated data.

Conclusion There are strong synergies between Wave encoding and LORAKS, which enables Wave-LORAKS to achieve higher acceleration and more flexible sampling compared to Wave-CAIPI.

3. B. Zhao, J. P. Haldar, C. Liao, D. Ma, Y. Jiang, M. A. Griswold, K. Setsompop, L. L. Wald.
Optimal Experiment Design for Magnetic Resonance Fingerprinting: Cramer-Rao Bound Meets Spin Dynamics.
IEEE Transactions on Medical Imaging 38:844-861, 2019.
PubMed Central ID: In Process.

Magnetic resonance (MR) fingerprinting is a new quantitative imaging paradigm, which simultaneously acquires multiple MR tissue parameter maps in a single experiment. In this paper, we present an estimation-theoretic framework to perform experiment design for MR fingerprinting. Specifically, we describe a discrete-time dynamic system to model spin dynamics, and derive an estimation-theoretic bound, i.e., the Cramer-Rao bound (CRB), to characterize the signal-to-noise ratio (SNR) efficiency of an MR fingerprinting experiment. We then formulate an optimal experiment design problem, which determines a sequence of acquisition parameters to encode MR tissue parameters with the maximal SNR efficiency, while respecting the physical constraints and other constraints from the image decoding/reconstruction process. We evaluate the performance of the proposed approach with numerical simulations, phantom experiments, and in vivo experiments. We demonstrate that the optimized experiments substantially reduce data acquisition time and/or improve parameter estimation. For example, the optimized experiments achieve about a factor of two improvement in the accuracy of T2 maps, while keeping similar or slightly better accuracy of T1 maps. Finally, as a remarkable observation, we find that the sequence of optimized acquisition parameters appears to be highly structured rather than randomly/pseudo-randomly varying as is prescribed in the conventional MR fingerprinting experiments.

4. J. Li, J. P. Haldar, J. C. Mosher, D. R. Nair, J. A. Gonzalez-Martinez, R. M. Leahy.
Scalable and Robust Tensor Decomposition of Spontaneous Stereotactic EEG Data.
IEEE Transactions on Biomedical Engineering 66:1549-1558, 2019.
PubMed Central ID: In Process.

Objective: Identification of networks from resting brain signals is an important step in understanding the dynamics of spontaneous brain activity. We approach this problem using a tensor-based model. Methods: We develop a rank-recursive Scalable and Robust Sequential Canonical Polyadic Decomposition (SRSCPD) framework to decompose a tensor into several rank-1 components. Robustness and scalability are achieved using a warm start for each rank based on the results from the previous rank. Results: In simulations we show that SRSCPD consistently outperforms the multi-start alternating least square (ALS) algorithm over a range of ranks and signal-to-noise ratios (SNRs), with lower computation cost. When applying SRSCPD to resting in-vivo stereotactic EEG (SEEG) data from two subjects with epilepsy, we found components corresponding to default mode and motor networks in both subjects. These components were also highly consistent within subject between two sessions recorded several hours apart. Similar components were not obtained using the conventional ALS algorithm. Conclusion: Consistent brain networks and their dynamic behaviors were identified from resting SEEG data using SRSCPD. Significance: SRSCPD is scalable to large datasets and therefore a promising tool for identification of brain networks in long recordings from single subjects.

#### 2018

1. B. Kim, B. E. Fisher, N. Schweighofer, R. M. Leahy, J. P. Haldar, S. Choi, D. B. Kay, J. Gordon, C. J. Winstein.
A Comparison of Seven Different DTI-derived Estimates of Corticospinal Tract Structural Characteristics in Chronic Stroke Survivors.
Journal of Neuroscience Methods 304:66-75, 2018.
PubMed Central ID: PMC5984168.

Background Different diffusion tensor imaging (DTI) has been used to estimate corticospinal tract (CST) structure in the context of stroke rehabilitation research. However, there is no gold standard for the estimate of CST structure in chronic stroke survivors. This study aims to determine the most accurate DTI-derived CST estimate that is associated with a clinical motor outcome measure.

Methods We obtained imaging and behavioral data from a phase-I stroke rehabilitation clinical trial. We included thirty-seven chronic stroke survivors with mild­to­moderate motor impairment. Imaging data were processed using BrainSuite16a software. We calculated mean FA for each of 7 different ROIs/VOIs that include manually drawn 2-D ROIs and 3-D VOIs of CST from individual tractography or standard atlas. We compared ipsi- and contralesional CST FA for each method. Partial correlation was conducted between each CST FA asymmetry index and a time-based motor outcome measure, controlling for age and chronicity.

Results Ipsilesional CST FA was significantly lower than contralesional CST FA for each of the 7 methods Only CST FA asymmetry from the 3-D individual CST tractography showed a significant correlation with the primary motor outcome (r=0.46, p=.005), while CST FA from the other six methods did not.

Comparison with existing methods Compared to the six other methods, CST FA asymmetry from 3-D individual tractography is the most accurate estimate of CST structure in this cohort of stroke survivors.

Conclusion We recommend this method for future research seeking to understand brain-behavior mechanisms of motor recovery in chronic stroke survivors.

2. R. A. Lobos, T. H. Kim, W. S. Hoge, J. P. Haldar.
Navigator-free EPI Ghost Correction with Structured Low-Rank Matrix Models: New Theory and Methods.
IEEE Transactions on Medical Imaging 37:2390-2402, 2018.
PubMed Central ID: In Process.
[toggle abstract] [link] [preprint] [related software]

Many EPI ghost correction methods are based on treating subsets of EPI data from different readout gradient polarities or different shots as if they were acquired from different "virtual coils" in a parallel imaging experiment. Structured low-rank matrix models have previously been introduced to enable calibrationless parallel imaging reconstruction, and such ideas have recently been extended to enable navigator-free EPI ghost correction. However, our theoretical analysis shows that, because of uniform subsampling, the corresponding optimization problems for EPI data will always have either undesirable or non-unique solutions in the absence of additional constraints. This theoretical analysis leads us to propose new problem formulations for navigator-free EPI that incorporate side information from either image-domain or k-space domain parallel imaging methods. The importance of using nonconvex low-rank matrix regularization is also identified. We demonstrate using phantom and in vivo data that the proposed methods are able to eliminate ghost artifacts for several navigator-free EPI acquisition schemes, obtaining better performance in comparison to state-of-the-art methods across a range of different scenarios, including both single-channel acquisition and highly accelerated multi-channel acquisition.

3. B. Bilgic, T. H. Kim, C. Liao, M. K. Manhard, L. L. Wald, J. P. Haldar, K. Setsompop.
Improving Parallel Imaging by Jointly Reconstructing Multi-Contrast Data.
Magnetic Resonance in Medicine 80:619-632, 2018.
PubMed Central ID: PMC5910232.
Editor's Pick, August 2018. [Highlights Interview] [Audioslides]

Purpose To develop parallel imaging techniques that simultaneously exploit coil sensitivity encoding, image phase prior information, similarities across multiple images, and complementary k-space sampling for highly accelerated data acquisition.

Methods We introduce joint virtual coil (JVC)-generalized autocalibrating partially parallel acquisitions (GRAPPA) to jointly reconstruct data acquired with different contrast preparations, and show its application in 2D, 3D, and simultaneous multi-slice (SMS) acquisitions. We extend the joint parallel imaging concept to exploit limited support and smooth phase constraints through Joint (J-) LORAKS formulation. J-LORAKS allows joint parallel imaging from limited autocalibration signal region, as well as permitting partial Fourier sampling and calibrationless reconstruction.

Results We demonstrate highly accelerated 2D balanced steady-state free precession with phase cycling, SMS multi-echo spin echo, 3D multi-echo magnetization-prepared rapid gradient echo, and multi-echo gradient recalled echo acquisitions in vivo. Compared to conventional GRAPPA, proposed joint acquisition/reconstruction techniques provide more than 2-fold reduction in reconstruction error.

Conclusion JVC-GRAPPA takes advantage of additional spatial encoding from phase information and image similarity, and employs different sampling patterns across acquisitions. J-LORAKS achieves a more parsimonious low-rank representation of local k-space by considering multiple images as additional coils. Both approaches provide dramatic improvement in artifact and noise mitigation over conventional single-contrast parallel imaging reconstruction.

4. A. Habibi, A. Damasio, B. Ilari, R. Veiga, A. A. Joshi, R. M. Leahy, J. P. Haldar, D. Varadarajan, C. Bhushan, H. Damasio.
Childhood Music Training Induces Change in Micro and Macroscopic Brain Structure: Results from a Longitudinal Study.
Cerebral Cortex 28:4336-4347, 2018.
PubMed Central ID: In Process.

Several studies comparing adult musicians and nonmusicians have shown that music training is associated with structural brain differences. It is not been established, however, whether such differences result from pre-existing biological traits, lengthy musical training, or an interaction of the two factors, or if comparable changes can be found in children undergoing music training. As part of an ongoing longitudinal study, we investigated the effects of music training on the developmental trajectory of children's brain structure, over two years, beginning at age 6. We compared these children with children of the same socio-economic background but either involved in sports training or not involved in any systematic after school training. We established at the onset that there were no pre-existing structural differences among the groups. Two years later we observed that children in the music group showed (1) a different rate of cortical thickness maturation between the right and left posterior superior temporal gyrus, and (2) higher fractional anisotropy in the corpus callosum, specifically in the crossing pathways connecting superior frontal, sensory, and motor segments. We conclude that music training induces macro and microstructural brain changes in school-age children, and that those changes are not attributable to pre-existing biological traits.

#### 2017

1. D. Varadarajan, J. P. Haldar.
A Theoretical Signal Processing Framework for Linear Diffusion MRI: Implications for Parameter Estimation and Experiment Design.
NeuroImage 161:206-218, 2017.
PubMed Central ID: PMC5696014.

The data measured in diffusion MRI can be modeled as the Fourier transform of the Ensemble Average Propagator (EAP), a probability distribution that summarizes the molecular diffusion behavior of the spins within each voxel. This Fourier relationship is potentially advantageous because of the extensive theory that has been developed to characterize the sampling requirements, accuracy, and stability of linear Fourier reconstruction methods. However, existing diffusion MRI data sampling and signal estimation methods have largely been developed and tuned without the benefit of such theory, instead relying on approximations, intuition, and extensive empirical evaluation. This paper aims to address this discrepancy by introducing a novel theoretical signal processing framework for diffusion MRI. The new framework can be used to characterize arbitrary linear diffusion estimation methods with arbitrary q-space sampling, and can be used to theoretically evaluate and compare the accuracy, resolution, and noise-resilience of different data acquisition and parameter estimation techniques. The framework is based on the EAP, and makes very limited modeling assumptions. As a result, the approach can even provide new insight into the behavior of model-based linear diffusion estimation methods in contexts where the modeling assumptions are inaccurate. The practical usefulness of the proposed framework is illustrated using both simulated and real diffusion MRI data in applications such as choosing between different parameter estimation methods and choosing between different q-space sampling schemes.

2. M. Chong, C. Bhushan, A. A. Joshi, S. Choi, J. P. Haldar, D. W. Shattuck, R. N. Spreng, R. M. Leahy.
Individual Parcellation of Resting fMRI with a Group Functional Connectivity Prior.
NeuroImage 156:87-100, 2017.
PubMed Central ID: PMC5774339.

Cortical parcellation based on resting fMRI is an important tool for investigating the functional organization and connectivity of the cerebral cortex. Group parcellation based on co-registration of anatomical images to a common atlas will inevitably result in errors in the locations of the boundaries of functional parcels when they are mapped back from the atlas to the individual. This is because areas of functional specialization vary across individuals in a manner that cannot be fully determined from the sulcal and gyral anatomy that is used for mapping between atlas and individual. We describe a method that avoids this problem by refining an initial group parcellation so that for each subject the parcel boundaries are optimized with respect to that subject's resting fMRI. Initialization with a common parcellation results in automatic correspondence between parcels across subjects. Further, by using a group sparsity constraint to model connectivity, we exploit group similarities in connectivity between parcels while optimizing their boundaries for each individual. We applied this approach with initialization on both high and low density group cortical parcellations and used resting fMRI data to refine across a group of individuals. Cross validation studies show improved homogeneity of resting activity within the refined parcels. Comparisons with task-based localizers show consistent reduction of variance of statistical parametric maps within the refined parcels relative to the group-based initialization indicating improved delineation of regions of functional specialization. This method enables a more accurate estimation of individual subject functional areas, facilitating group analysis of functional connectivity, while maintaining consistency across individuals with a standardized topological atlas.

3. D. Kim, E. K. Doyle, J. L. Wisnowski, J. H. Kim, J. P. Haldar.
Diffusion-Relaxation Correlation Spectroscopic Imaging: A Multidimensional Approach for Probing Microstructure.
Magnetic Resonance in Medicine 78:2236-2249, 2017.
PubMed Central ID: PMC5605406.

Purpose To propose and evaluate a novel multidimensional approach for imaging sub-voxel tissue compartments called Diffusion-Relaxation Correlation Spectroscopic Imaging (DR-CSI).

Theory and Methods Multi-exponential modeling of MR diffusion or relaxation data is commonly used to infer the many different microscopic tissue compartments that contribute signal to macroscopic MR imaging voxels. However, multi-exponential estimation is known to be difficult and ill-posed. Observing that this ill-posedness is theoretically reduced in higher dimensions, DR-CSI uses a novel multidimensional imaging experiment that jointly encodes diffusion and relaxation information, and then uses a novel constrained reconstruction technique to generate a multidimensional diffusion-relaxation correlation spectrum for every voxel. The peaks of the multidimensional spectrum are expected to correspond to the distinct tissue microenvironments that are present within each macroscopic imaging voxel.

Results Using numerical simulations, experiment data from a custom-built phantom, and experiment data from a mouse model of traumatic spinal cord injury, DR-CSI is demonstrated to provide substantially better multi-compartment resolving power compared to conventional diffusion- and relaxation-based methods.

Conclusion The DR-CSI approach provides powerful new capabilities for resolving the different components of multi-compartment tissue models, and can be leveraged to significantly expand the insights provided by MRI in studies of tissue microstructure.

4. T. H. Kim, K. Setsompop, J. P. Haldar.
LORAKS Makes Better SENSE: Phase-Constrained Partial Fourier SENSE Reconstruction without Phase Calibration.
Magnetic Resonance in Medicine 77:1021-1035, 2017.
PubMed Central ID: PMC5045741.

Purpose Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information.

Theory and Methods The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories.

Results Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches.

Conclusion The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI.

#### 2016

1. C. Bhushan, M. Chong, S. Choi, A. A. Joshi, J. P. Haldar, H. Damasio, R. M. Leahy.
Non-local means filtering reveals real-time whole-brain cortical interactions in resting fMRI.
PLOS ONE 11:e0158504, 2016.
PubMed Central ID: PMC4938391.

Intensity variations over time in resting BOLD fMRI exhibit spatial correlation patterns consistent with a set of large scale cortical networks. However, visualizations of this data on the brain surface, even after extensive preprocessing, are dominated by local intensity fluctuations that obscure larger scale behavior. Our novel adaptation of non-local means (NLM) filtering, which we refer to as temporal NLM or tNLM, reduces these local fluctuations without the spatial blurring that occurs when using standard linear filtering methods. We show examples of tNLM filtering that allow direct visualization of spatio-temporal behavior on the cortical surface. These results reveal patterns of activity consistent with known networks as well as more complex dynamic changes within and between these networks. This ability to directly visualize brain activity may facilitate new insights into spontaneous brain dynamics. Further, temporal NLM can also be used as a preprocessor for resting fMRI for exploration of dynamic brain networks. We demonstrate its utility through application to graph-based functional cortical parcellation. Simulations with known ground truth functional regions demonstrate that tNLM filtering prior to parcellation avoids the formation of false parcels that can arise when using linear filtering. Application to resting fMRI data from the Human Connectome Project shows significant improvement, in comparison to linear filtering, in quantitative agreement with functional regions identified independently using task-based experiments as well as in test-retest reliability.

2. D. Kim, J. P. Haldar.
Greedy Algorithms for Nonnegativity-Constrained Simultaneous Sparse Recovery.
Signal Processing 125:274-289, 2016.
PubMed Central ID: PMC4784713.

This work proposes a family of greedy algorithms to jointly reconstruct a set of vectors that are (i) nonnegative and (ii) simultaneously sparse with a shared support set. The proposed algorithms generalize previous approaches that were designed to impose these constraints individually. Similar to previous greedy algorithms for sparse recovery, the proposed algorithms iteratively identify promising support indices. In contrast to previous approaches, the support index selection procedure has been adapted to prioritize indices that are consistent with both the nonnegativity and shared support constraints. Empirical results demonstrate for the first time that the combined use of simultaneous sparsity and nonnegativity constraints can substantially improve recovery performance relative to existing greedy algorithms that impose less signal structure.

3. J. P. Haldar, J. Zhuo.
P-LORAKS: Low-Rank Modeling of Local k-Space Neighborhoods with Parallel Imaging Data.
Magnetic Resonance in Medicine 75:1499-1514, 2016.
PubMed Central ID: PMC4637005.
[toggle abstract] [link] [preprint] [related software]

Purpose To propose and evaluate P-LORAKS, a new calibrationless parallel imaging reconstruction framework.

Theory and Methods LORAKS is a flexible and powerful framework that was recently proposed for constrained MRI reconstruction. LORAKS was based on the observation that certain matrices constructed from fully-sampled k-space data should have low rank whenever the image has limited support or smooth phase, and made it possible to accurately reconstruct images from undersampled or noisy data using low-rank regularization. This paper introduces P-LORAKS, which extends LORAKS to the context of parallel imaging. This is achieved by combining the LORAKS matrices from different channels to yield a larger but more parsimonious low-rank matrix model of parallel imaging data. This new model can be used to regularize the reconstruction of undersampled parallel imaging data, and implicitly imposes phase, support, and parallel imaging constraints without needing to calibrate phase, support, or sensitivity profiles.

Results The capabilities of P-LORAKS are evaluated with retrospectively undersampled data and compared against existing parallel MRI reconstruction methods. Results show that P-LORAKS can improve parallel imaging reconstruction quality, and can enable the use of new k-space trajectories that are not compatible with existing reconstruction methods.

Conclusion The P-LORAKS framewok provides a new and effective way to regularize parallel imaging reconstruction.

4. J. H. Kim, S.-K. Song, J. P. Haldar.
Signal-to-Noise Ratio-Enhancing Joint Reconstruction for Improved Diffusion Imaging of Mouse Spinal Cord White Matter Injury.
Magnetic Resonance in Medicine 75:852-858, 2016.
PubMed Central ID: PMC4589425.

Purpose To assess the capability of signal-to-noise ratio enhancing reconstruction (SER) to reduce the acquisition time for quantitative white matter injury assessment.

Methods Four single-average diffusion tensor imaging (DTI) datasets were acquired for each animal from 4 mouse cohorts: two models of spinal cord injury and two control groups. Quantitative parameters (apparent diffusion coefficient, relative anisotropy, axial and radial diffusivities) were computed from (I) single-average data with traditional reconstruction; (II) single-average data with SER; (III) 4-average data with traditional reconstruction; and (IV) single-average data with optimized multicomponent nonlocal means (OMNLM) denoising. These approaches were compared based on coefficients of variation (COVs) and whether estimated diffusion parameters were sensitive to injury.

Results SER yielded better COVs for diffusivity and anisotropy than traditional reconstruction of single-average data, and yielded comparable COVs to that achieved with 4-average data. In addition, diffusion parameters obtained using SER with single-average data had comparable injury sensitivity to those obtained from 4-average data, while diffusion parameters obtained from OMNLM and traditional reconstruction of single-average data had limited sensitivity.

Conclusion A 4-fold reduction in the number of averages for quantitative diffusion imaging of small animal white matter injury is feasible using SER. Our results also underscore the need to validate nonlinear methods using task-based measures on an application-by-application basis.

#### 2015

1. D. Varadarajan, J. P. Haldar.
A Majorize-Minimize Framework for Rician and Non-Central Chi MR Images.
IEEE Transactions on Medical Imaging 34:2191-2202, 2015.
PubMed Central ID: PMC4596756.

The statistics of many MR magnitude images are described by the non-central chi (NCC) family of probability distributions, which includes the Rician distribution as a special case. These distributions have complicated negative log-likelihoods that are nontrivial to optimize. This paper describes a novel majorize-minimize framework for NCC data that allows penalized maximum likelihood estimates to be obtained by solving a series of much simpler regularized least-squares surrogate problems. The proposed framework is general and can be useful in a range of applications. We illustrate the potential advantages of the framework with real and simulated data in two contexts: 1) MR image denoising and 2) diffusion profile estimation in high angular resolution diffusion MRI. The proposed approach is shown to yield improved results compared to methods that model the noise statistics inaccurately and faster computation relative to commonly-used nonlinear optimization techniques.

2. C. Bhushan, J. P. Haldar, S. Choi, A. A. Joshi, D. W. Shattuck, R. M. Leahy.
Co-registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization.
NeuroImage 115:269-280, 2015.
PubMed Central ID: PMC4461504.

Diffusion MRI provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain. Echo planar imaging (EPI) sequences, which are frequently used for acquisition of diffusion images, are sensitive to inhomogeneities in the primary magnetic (B0) field that cause localized distortions in the reconstructed images. We describe and evaluate a new method for correction of susceptibility-induced distortion in diffusion images in the absence of an accurate B0 fieldmap. In our method, the distortion field is estimated using a constrained non-rigid registration between an undistorted T1-weighted anatomical image and one of the distorted EPI images from diffusion acquisition. Our registration framework is based on a new approach, INVERSION (Inverse contrast Normalization for VERy Simple registratION), which exploits the inverted contrast relationship between T1- and T2-weighted brain images to define a simple and robust similarity measure. We also describe how INVERSION can be used for rigid alignment of diffusion images and T1-weighted anatomical images. Our approach is evaluated with multiple in vivo datasets acquired with a different acquisition parameters. Compared to other methods, INVERSION shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non-rigid distortion correction.

#### 2014

1. A. Habibi, B. Ilari, K. Crimi, M. Metke, J. T. Kaplan, A. A. Joshi, R. M. Leahy, D. W. Shattuck, S. Y. Choi, J. P. Haldar, B. Ficek, A. Damasio, H. Damasio.
An Equal Start: Absence of Group Differences in Cognitive, Social and Neural Measures Prior to Music or Sports Training in Children.
Frontiers in Human Neuroscience 8:690, 2014.
PubMed Central ID: PMC4158792.

Several studies comparing adult musicians and non-musicians have provided compelling evidence for functional and anatomical differences in the brain systems engaged by musical training. It is not known, however, whether those differences result from long term musical training or from pre-existing traits favoring musicality. In an attempt to begin addressing this question, we have launched a longitudinal investigation of the effects of childhood music training on cognitive, social and neural development. We compared a group of 6-7 year old children at the start of intense after-school musical training, with two groups of children: one involved in high intensity sports training but not musical training, another not involved in any systematic training. All children were tested with a comprehensive battery of cognitive, motor, musical, emotional and social assessments and underwent magnetic resonance imaging and electroencephalography. Our first objective was to determine whether children who participate in musical training were different, prior to training, from children in the control groups in terms of cognitive, motor, musical, emotional and social behavior measures as well as in structural and functional brain measures. Our second objective was to determine whether musical skills, as measured by a music perception assessment prior to training, correlates with emotional and social outcome measures that have been shown to be associated with musical training. We found no neural, cognitive, motor, emotional or social differences among the three groups. In addition, there was no correlation between music perception skills and any of the social or emotional measures. These results provide a baseline for an ongoing longitudinal investigation of the effects of music training.

2. J. P. Haldar.
Low-Rank Modeling of Local k-Space Neighborhoods (LORAKS) for Constrained MRI.
IEEE Transactions on Medical Imaging 33:668-681, 2014.
PubMed Central ID: PMC4122573.
[toggle abstract] [link] [preprint] [related software]

Recent theoretical results on low-rank matrix reconstruction have inspired significant interest in low-rank modeling of MRI images. Existing approaches have focused on higher-dimensional scenarios with data available from multiple channels, timepoints, or image contrasts. The present work demonstrates that single-channel, single-contrast, single-timepoint k-space data can also be mapped to low-rank matrices when the image has limited spatial support or slowly varying phase. Based on this, we develop a novel and flexible framework for constrained image reconstruction that uses low-rank matrix modeling of local k-space neighborhoods (LORAKS). A new regularization penalty and corresponding algorithm for promoting low-rank are also introduced. The potential of LORAKS is demonstrated with simulated and experimental data for a range of denoising and sparse-sampling applications. LORAKS is also compared against state-of-the-art methods like homodyne reconstruction, l1-norm minimization, and total variation minimization, and is demonstrated to have distinct features and advantages. In addition, while calibration-based support and phase constraints are commonly used in existing methods, the LORAKS framework enables calibrationless use of these constraints.

3. C. Bhushan, A. A. Joshi, R. M. Leahy, J. P. Haldar.
Improved B0-distortion correction in diffusion MRI using interlaced q-space sampling and constrained reconstruction.
Magnetic Resonance in Medicine 72:1218-1232, 2014.
PubMed Central ID: PMC4017008.

Purpose To enable high-quality correction of susceptibility-induced geometric distortion artifacts in diffusion magnetic resonance imaging (MRI) images without increasing scan time.

Theory and Methods A new method for distortion correction is proposed based on subsampling a generalized version of the state-of-the-art reversed-gradient distortion correction method. Rather than acquire each q-space sample multiple times with different distortions (as in the conventional reversed-gradient method), we sample each q-space point once with an interlaced sampling scheme that measures different distortions at different q-space locations. Distortion correction is achieved using a novel constrained reconstruction formulation that leverages the smoothness of diffusion data in q-space.

Results The effectiveness of the proposed method is demonstrated with simulated and in vivo diffusion MRI data. The proposed method is substantially faster than the reversed-gradient method, and can also provide smaller intensity errors in the corrected images and smaller errors in derived quantitative diffusion parameters.

Conclusion The proposed method enables state-of-the-art distortion correction performance without increasing data acquisition time.

4. Y. Lin, J. P. Haldar, Q. Li, P. S. Conti, R. M. Leahy.
Sparsity Constrained Mixture Modeling for the Estimation of Kinetic Parameters in Dynamic PET.
IEEE Transactions on Medical Imaging 33:173-185, 2014.
PubMed Central ID: PMC4013253.

The estimation and analysis of kinetic parameters in dynamic PET is frequently confounded by tissue heterogeneity and partial volume effects. We propose a new constrained model of dynamic PET to address these limitations. The proposed formulation incorporates an explicit mixture model in which each image voxel is represented as a mixture of different pure tissue types with distinct temporal dynamics.We use Cramér-Rao lower bounds to demonstrate that the use of prior information is important to stabilize parameter estimation with this model. As a result, we propose a constrained formulation of the estimation problem that we solve using a two-stage algorithm. In the first stage, a sparse signal processing method is applied to estimate the rate parameters for the different tissue compartments from the noisy PET time series. In the second stage, tissue fractions and the linear parameters of different time activity curves are estimated using a combination of spatial-regularity and fractional mixture constraints. A block coordinate descent algorithm is combined with a manifold search to robustly estimate these parameters. The method is evaluated with both simulated and experimental dynamic PET data.

5. F. Lam, S. D. Babacan, J. P. Haldar, M. W. Weiner, N. Schuff, Z.-P. Liang.
Denoising Diffusion-Weighted Magnitude MR Images using Rank and Edge Constraints.
Magnetic Resonance in Medicine 71:1272-1284, 2014.
PubMed Central ID: PMC3796128.

Purpose To improve signal-to-noise ratio for diffusion-weighted magnetic resonance images.

Methods A new method is proposed for denoising diffusion-weighted magnitude images. The proposed method formulates the denoising problem as an maximum a posteriori estimation problem based on Rician/noncentral chi likelihood models, incorporating an edge prior and a low-rank model. The resulting optimization problem is solved efficiently using a half-quadratic method with an alternating minimization scheme.

Results The performance of the proposed method has been validated using simulated and experimental data. Diffusion-weighted images and noisy data were simulated based on the diffusion tensor imaging model and Rician/noncentral chi distributions. The simulation study (with known gold standard) shows substantial improvements in single-to-noise ratio and diffusion tensor estimation after denoising. In vivo diffusion imaging data at different b-values were acquired. Based on the experimental data, qualitative improvement in image quality and quantitative improvement in diffusion tensor estimation were demonstrated. Additionally, the proposed method is shown to outperform one of the state-of-the-art nonlocal means-based denoising algorithms, both qualitatively and quantitatively.

Conclusion The signal-to-noise ratio of diffusion-weighted images can be effectively improved with rank and edge constraints, resulting in an improvement in diffusion parameter estimation accuracy.

#### 2013

1. S. Ashrafulla, J. P. Haldar, A. A. Joshi, R. M. Leahy.
Canonical Granger Causality between Regions of Interest.
NeuroImage 83:189-199, 2013.
PubMed Central ID: PMC4026328.

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors, voxels, or vertices despite the fact that a single region of interest will often include multiple such recordings. In this paper, we present a novel measure of interaction between regions of interest rather than individual signals. The proposed measure,termed canonical Granger causality, combines ideas from canonical correlation and Granger causality analysis to yield a measure that reflects directed causality between two regions of interest. In particular, canonical Granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario. The optimized linear combinations are obtained using a variation of a technique developed for optimization on the Steifel manifold. We demonstrate the advantages of canonical Granger causality in comparison to alternative causality measures for a range of different simulated datasets. We also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task. Results demonstrate that canonical Granger causality can be used to identify causal relationships between striate and prestriate cortex in cases where standard Granger causality is unable to identify statistically significant interactions.

2. J. P. Haldar, R. M. Leahy.
Linear Transforms for Fourier Data on the Sphere: Application to High Angular Resolution Diffusion MRI of the Brain.
NeuroImage 71:233-247, 2013.
PubMed Central ID: PMC3594568.
[toggle abstract] [link] [preprint] [related software]

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors.

3. J. Gai, N. Obeid, J. L. Holtrop, X.-L. Wu, F. Lam, M. Fu, J. P. Haldar, W.-m. W. Hwu, Z.-P. Liang, B. P. Sutton.
More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPUs.
Journal of Parallel and Distributed Computing 73:686-697, 2013.
PubMed Central ID: PMC3652469.

Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code.

4. J. P. Haldar, V. J. Wedeen, M. Nezamzadeh, G. Dai, M. W. Weiner, N. Schuff, Z.-P. Liang.
Improved Diffusion Imaging through SNR-Enhancing Joint Reconstruction.
Magnetic Resonance in Medicine 69:277-289, 2013.
PubMed Central ID: PMC3407310.
[toggle abstract] [link] [preprint] [related software]

Quantitative diffusion imaging is a powerful technique for the characterization of complex tissue microarchitecture. However, long acquisition times and limited signal-to-noise ratio (SNR) represent significant hurdles for many in vivo applications. This paper presents a new approach to reduce noise while largely maintaining resolution in diffusion weighted images, using a statistical reconstruction method that takes advantage of the high level of structural correlation observed in typical datasets. Compared to existing denoising methods, the proposed method performs reconstruction directly from the measured complex k-space data, allowing for Gaussian noise modeling and theoretical characterizations of the resolution and SNR of the reconstructed images. In addition, the proposed method is compatible with many different models of the diffusion signal (e.g., diffusion tensor modeling, q-space modeling, etc.). The joint reconstruction method can provide significant improvements in SNR relative to conventional reconstruction techniques, with a relatively minor corresponding loss in image resolution. Results are shown in the context of diffusion spectrum imaging tractography and diffusion tensor imaging, illustrating the potential of this SNR-enhancing joint reconstruction approach for a range of different diffusion imaging experiments.

#### 2012

1. B. Zhao, J. P. Haldar, A. G. Christodoulou, Z.-P. Liang.
Image Reconstruction from Highly Undersampled (k,t)-Space Data with Joint Partial Separability and Sparsity Constraints.
IEEE Transactions on Medical Imaging 31:1809-1820, 2012.
PubMed Central ID: PMC3434301.

Partial separability (PS) and sparsity have been previously used to enable reconstruction of dynamic images from undersampled (k,t)-space data. This paper presents a new method to use PS and sparsity constraints jointly for enhanced performance in this context. The proposed method combines the complementary advantages of PS and sparsity constraints using a unified formulation, achieving significantly better reconstruction performance than using either of these constraints individually. A globally-convergent computational algorithm is described to efficiently solve the underlying optimization problem. Reconstruction results from simulated and in vivo cardiac MRI data are also shown to illustrate the performance of the proposed method.

#### 2011

1. Y. Wang, Q. Wang, J. P. Haldar, F.-C. Yeh, M. Xie, P. Sun, T.-W. Tu, K. Trinkaus, R. S. Klein, A. H. Cross, S.-K. Song.
Quantification of increased cellularity during inflammatory demyelination.
Brain 134:3587-3598, 2011.
PubMed Central ID: PMC3235568.

Multiple sclerosis is characterized by inflammatory demyelination and irreversible axonal injury leading to permanent neurological disabilities. Diffusion tensor imaging demonstrates an improved capability over standard magnetic resonance imaging to differentiate axon from myelin pathologies. However, the increased cellularity and vasogenic oedema associated with inflammation cannot be detected or separated from axon/myelin injury by diffusion tensor imaging, limiting its clinical applications. A novel diffusion basis spectrum imaging, capable of characterizing water diffusion properties associated with axon/myelin injury and inflammation, was developed to quantitatively reveal white matter pathologies in central nervous system disorders. Tissue phantoms made of normal fixed mouse trigeminal nerves juxtaposed with and without gel were employed to demonstrate the feasibility of diffusion basis spectrum imaging to quantify baseline cellularity in the absence and presence of vasogenic oedema. Following the phantom studies, in vivo diffusion basis spectrum imaging and diffusion tensor imaging with immunohistochemistry validation were performed on the corpus callosum of cuprizone treated mice. Results demonstrate that in vivo diffusion basis spectrum imaging can effectively separate the confounding effects of increased cellularity and/or grey matter contamination, allowing successful detection of immunohistochemistry confirmed axonal injury and/or demyelination in middle and rostral corpus callosum that were missed by diffusion tensor imaging. In addition, diffusion basis spectrum imaging-derived cellularity strongly correlated with numbers of cell nuclei determined using immunohistochemistry. Our findings suggest that diffusion basis spectrum imaging has great potential to provide non-invasive biomarkers for neuroinflammation, axonal injury and demyelination coexisting in multiple sclerosis.

2. J. P. Haldar, Z. Wang, G. Popescu, Z.-P. Liang.
Deconvolved Spatial Light Interference Microscopy for Live Cell Imaging.
IEEE Transactions on Biomedical Engineering 58:2489-2497, 2011.
PubMed Central ID: PMC3286342.
[toggle abstract] [link] [toggle errata] [preprint]

Spatial light interference microscopy (SLIM) is a recently-developed method for the label-free imaging of live cells, using the quantitative optical path length through the sample as an endogenous source of contrast. In conventional SLIM, spatial resolution is limited by diffraction and aberrations. This paper describes a novel constrained deconvolution method for improving resolution in SLIM. Constrained deconvolution is enabled by experimental measurement of the system point-spread function and the modeling of coherent image formation in SLIM. Results using simulated and experimental data demonstrate that the proposed method leads to significant improvements in the resolution and contrast of SLIM images. The proposed method should prove useful for high-resolution label-free studies of biological cells and sub-cellular processes.

3.       A few of our corrections to the manuscript proofs were misinterpreted by the publisher, and we were not shown a final version of the paper prior to publication. The preprint is correct. Errors persisting in the published version include confusions between the symbols $$\Phi$$, $$\boldsymbol{\phi}$$, and $$\boldsymbol{\upphi}$$ (a bold roman version of $$\phi$$), and confusions between the symbols $$\Psi$$, $$\boldsymbol{\psi}$$, and $$\boldsymbol{\uppsi}$$ (a bold roman version of $$\psi$$). Please contact me if you'd like a copy of our original manuscript (with the correct mathematical symbols).

4. D. Hernando, D. C. Karampinos, K. F. King, J. P. Haldar, S. Majumdar, J. G. Georgiadis, Z.-P. Liang.
Removal of olefinic fat chemical shift artifact in diffusion MRI.
Magnetic Resonance in Medicine 65:692-701, 2011.
PubMed Central ID: PMC3069507.

Diffusion-weighted (DW) MRI has emerged as a key tool for assessing the microstructure of tissues in healthy and diseased states. Because of its rapid acquisition speed and insensitivity to motion, single-shot echo-planar imaging is the most common DW imaging technique. However, the presence of fat signal can severely affect DW-echo planar imaging acquisitions because of the chemical shift artifact. Fat suppression is usually achieved through some form of chemical shift-based fat saturation. Such methods effectively suppress the signal originating from aliphatic fat protons, but fail to suppress the signal from olefinic protons. Olefinic fat signal may result in significant distortions in the DW images, which bias the subsequently estimated diffusion parameters. This article introduces a method for removing olefinic fat signal from DW images, based on an echo time-shifted acquisition. The method is developed and analyzed specifically in the context of single-shot DW-echo-planar imaging, where image phase is generally unreliable. The proposed method is tested with phantom and in vivo datasets, and compared with a standard acquisition to demonstrate its performance.

5. J. P. Haldar, D. Hernando, Z.-P. Liang.
Compressed-Sensing MRI with Random Encoding.
IEEE Transactions on Medical Imaging 30:893-903, 2011.
PubMed Central ID: PMC3271122.
[toggle abstract] [link] [toggle errata] [preprint]
Correction to "Compressed-Sensing MRI with Random Encoding."
IEEE Transactions on Medical Imaging 32:1362, 2013.

Compressed sensing (CS) has the potential to reduce MR data acquisition time. In order for CS-based imaging schemes to be effective, the signal of interest should be sparse or compressible in a known representation, and the measurement scheme should have good mathematical properties with respect to this representation. While MR images are often compressible, the second requirement is often only weakly satisfied with respect to commonly used Fourier encoding schemes. This paper investigates the use of random encoding for CS-MRI, in an effort to emulate the "universal" encoding schemes suggested by the theoretical CS literature. This random encoding is achieved experimentally with tailored spatially-selective RF pulses. Both simulation and experimental studies were conducted to investigate the imaging properties of this new scheme with respect to Fourier schemes. Results indicate that random encoding has the potential to outperform conventional encoding in certain scenarios. However, our study also indicates that random encoding fails to satisfy theoretical sufficient conditions for stable and accurate CS reconstruction in many scenarios of interest. Therefore, there is still no general theoretical performance guarantee for CS-MRI, with or without random encoding, and CS-based methods should be developed and validated carefully in the context of specific applications.

The publisher introduced an error in Equation 4 during the final stages of publication, and this error was not caught in the final proofs. The preprint is correct. Equation 4 should read: $$\alpha_s \left\|\mathbf{x}\right\|_{\ell_2}^2 \leq \left\| \mathbf{\Phi} \mathbf{x} \right\|_{\ell_2}^2 \leq \beta_s \left\|\mathbf{x}\right\|_{\ell_2}^2$$

#### 2010

1. R. John, R. Rezaeipoor, S. G. Adie, E. J. Chaney, A. L. Oldenburg, M. Marjanovic, J. P. Haldar, B. P. Sutton, S. A. Boppart.
In vivo magnetomotive optical molecular imaging using targeted magnetic nanoprobes.
Proceedings of the National Academy of Sciences of the United States of America 107:8085-8090, 2010.
PubMed Central ID: PMC2889582.

Dynamic magnetomotion of magnetic nanoparticles (MNPs) detected with magnetomotive optical coherence tomography (MM-OCT) represents a new methodology for contrast enhancement and therapeutic interventions in molecular imaging. In this study, we demonstrate in vivo imaging of dynamic functionalized iron oxide MNPs using MM-OCT in a preclinical mammary tumor model. Using targeted MNPs, in vivo MM-OCT images exhibit strong magnetomotive signals in mammary tumor, and no significant signals were measured from tumors of rats injected with nontargeted MNPs or saline. The results of in vivo MM-OCT are validated by MRI, ex vivo MM-OCT, Prussian blue staining of histological sections, and immunohistochemical analysis of excised tumors and internal organs. The MNPs are antibody functionalized to target the human epidermal growth factor receptor 2 (HER2 neu) protein. Fc-directed conjugation of the antibody to the MNPs aids in reducing uptake by macrophages in the reticulo-endothelial system, thereby increasing the circulation time in the blood. These engineered magnetic nanoprobes have multifunctional capabilities enabling them to be used as dynamic contrast agents in MM-OCT and MRI.

2. D. Hernando, P. Kellman, J. P. Haldar, Z.-P. Liang.
Robust water/fat separation in the presence of large field inhomogeneities using a graph cut algorithm.
Magnetic Resonance in Medicine 63:79-90, 2010.
PubMed Central ID: PMC3414226.
Recipient of the ISMRM 2009 I. I. Rabi Young Investigator Award.

Water/fat separation is a classical problem for in vivo proton MRI. Although many methods have been proposed to address this problem, robust water/fat separation remains a challenge, especially in the presence of large amplitude of static field inhomogeneities. This problem is challenging because of the nonuniqueness of the solution for an isolated voxel. This paper tackles the problem using a statistically motivated formulation that jointly estimates the complete field map and the entire water/fat images. This formulation results in a difficult optimization problem that is solved effectively using a novel graph cut algorithm, based on an iterative process where all voxels are updated simultaneously. The proposed method has good theoretical properties, as well as an efficient implementation. Simulations and in vivo results are shown to highlight the properties of the proposed method and compare it to previous approaches. Twenty-five cardiac datasets acquired on a short, wide-bore scanner with different slice orientations were used to test the proposed method, which produced robust water/fat separation for these challenging datasets. This paper also shows example applications of the proposed method, such as the characterization of intramyocardial fat.

#### 2009

1. J. P. Haldar, D. Hernando.
Rank-Constrained Solutions to Linear Matrix Equations using PowerFactorization.
IEEE Signal Processing Letters 16:584-587, 2009.
PubMed Central ID: PMC3290097.
[toggle abstract] [link] [preprint] [related software]

Algorithms to construct/recover low-rank matrices satisfying a set of linear equality constraints have important applications in many signal processing contexts. Recently, theoretical guarantees for minimum-rank matrix recovery have been proven for nuclear norm minimization (NNM), which can be solved using standard convex optimization approaches. While nuclear norm minimization is effective, it can be computationally demanding. In this work, we explore the use of the PowerFactorization (PF) algorithm as a tool for rank-constrained matrix recovery. Empirical results indicate that incremented-rank PF is significantly more successful than NNM at recovering low-rank matrices, in addition to being faster.

2. J. H. Kim, J. Haldar, Z.-P. Liang, S.-K. Song.
Diffusion Tensor Imaging of Mouse Brain Stem and Cervical Spinal Cord.
Journal of Neuroscience Methods 176:186-191, 2009.
PubMed Central ID: PMC2637387.

In vivo diffusion tensor imaging measurements of the mouse brain stem and cervical spinal cord are presented. Utilizing actively decoupled transmit/receive coils, high resolution diffusion images (117 x 59 x 500 μm3) were acquired at 4.7 T within an hour. Both brain stem and cervical spine displayed clear gray-white matter contrast. The cervical spinal cord white matter showed similar tissue characteristics as seen in the thoracic cord. The coherent fiber orientation in the white matter was observed in both the brain stem and the cervical spinal cord. The results may serve as a reference for future inter-lab comparison in mouse brain stem and cervical spine diffusion measurements.

#### 2008

1. S. S. Stone, J. P. Haldar, S. C. Tsao, W.-m. W. Hwu, B. P. Sutton, Z.-P. Liang.
Accelerating Advanced MRI Reconstructions on GPUs.
Journal of Parallel and Distributed Computing 68:1307-1318, 2008.
PubMed Central ID: PMC3142623.

Computational acceleration on graphics processing units (GPUs) can make advanced magnetic resonance imaging (MRI) reconstruction algorithms attractive in clinical settings, thereby improving the quality of MR images across a broad spectrum of applications. This paper describes the acceleration of such an algorithm on NVIDIA's Quadro FX 5600. The reconstruction of a 3D image with 1283 voxels achieves up to 180 GFLOPS and requires just over one minute on the Quadro, while reconstruction on a quad-core CPU is twenty-one times slower. Furthermore, for the data set studied in this article, the percent error exhibited by the advanced reconstruction is roughly three times lower than the percent error incurred by conventional reconstruction techniques.

2. J. P. Haldar, D. Hernando, S.-K. Song, Z.-P. Liang.
Anatomically Constrained Reconstruction from Noisy Data.
Magnetic Resonance in Medicine 59:810-818, 2008.
[toggle abstract] [link] [toggle errata] [preprint]

Noise is a major concern in many important imaging applications. To improve data signal-to-noise ratio (SNR), experiments often focus on collecting low-frequency k-space data. This article proposes a new scheme to enable extended k-space sampling in these contexts. It is shown that the degradation in SNR associated with extended sampling can be effectively mitigated by using statistical modeling in concert with anatomical prior information. The method represents a significant departure from most existing anatomically constrained imaging methods, which rely on anatomical information to achieve super-resolution. The method has the advantage that less accurate anatomical information is required relative to super-resolution approaches. Theoretical and experimental results are provided to characterize the performance of the proposed scheme.

A few of our corrections to the manuscript proofs were misinterpreted by the publisher, and we were not shown a final version of the paper prior to publication. The preprint is correct. Errors persisting in the published version include:

• Eq. 3, which should read $$\hat{\rho}\left(\mathbf{x}\right) = \rho\left(\mathbf{x}\right) * h\left(\mathbf{x}\right) + \bar{\eta}\left(\mathbf{x}\right)$$.

• Ref. 23 has no relationship with Leeds, United Kingdom.

3. D. Hernando, J. P. Haldar, B. P. Sutton, J. Ma, P. Kellman, Z.-P. Liang.
Joint Estimation of Water/Fat Images and Field Inhomogeneity Map.
Magnetic Resonance in Medicine 59:571-580, 2008.
PubMed Central ID: PMC3538139.

Water/fat separation in the presence of B0 field inhomogeneity is a problem of considerable practical importance in MRI. This article describes two complementary methods for estimating the water/fat images and the field inhomogeneity map from Dixon-type acquisitions. One is based on variable projection (VARPRO) and the other on linear prediction (LP). The VARPRO method is very robust and can be used in low signal-to-noise ratio conditions because of its ability to achieve the maximum-likelihood solution. The LP method is computationally more efficient, and is shown to perform well under moderate levels of noise and field inhomogeneity. These methods have been extended to handle multicoil acquisitions by jointly solving the estimation problem for all the coils. Both methods are analyzed and compared and results from several experiments are included to demonstrate their performance.

### Book Chapter

• Y. Zhuo, X.-L. Wu, J. P. Haldar, T. Marin, W.-m. Hwu, Z.-P. Liang, B. P. Sutton.
Using GPUs to Accelerate Advanced MRI Reconstruction with Field Inhomogeneity Compensation.
In GPU Computing Gems Emerald Edition, W.-m. W. Hwu Ed., Elsevier Inc., 2011, pp. 709-722.

Magnetic resonance imaging (MRI) is a flexible diagnostic tool, providing image contrast relating to the structure, function, and biochemistry of virtually every system in the body. However, the technique is generally slow and has low sensitivity, which limits its application in the clinical environment. Several significant advances in the past 10 years have created potential solutions to these problems, greatly increasing imaging speed and combining information from several acquisitions to increase sensitivity. But the computational time required for these new techniques has limited their use to research settings. In the clinic, images are needed at the conclusion of a scan to immediately decide if a subject moved, if the correct location was imaged, or if sufficient signal and contrast were obtained. Therefore, to achieve clinical relevance, it is necessary to accelerate the advanced MRI image reconstruction techniques.
In this chapter, we focus on a GPU implementation for a fast advanced non-Cartesian MRI reconstruction algorithm with field inhomogeneity compensation. The parallel structure of the reconstruction algorithms makes it suitable for parallel programming on GPUs. Accelerating this kind of algorithm can allow for more accurate image reconstruction while keeping computation times short enough for clinical use.

### Conference Proceedings

#### 2019

1. D. Varadarajan, J. P. Haldar.
Learning-Based Jointly-Optimal Design of the Diffusion Encoding Scheme and Orientation Estimation Method for Diffusion MRI.
International Society for Magnetic Resonance in Medicine 27th Annual Meeting, Montreal, 2019, p. 554. (abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

Diffusion MRI is powerful but limited by long scan times. When optimizing diffusion MRI, most previous methods have either optimized the encoding scheme (i.e., q-space samples) or have optimized the parameter estimation method. In this work, we propose and evaluate a novel approach that jointly optimizes both the encoding scheme and the estimation scheme. This is enabled by combining linear estimation theory with machine learning techniques. Our results show the strong potential of our new approach. Perhaps surprisingly and in contrast to conventional wisdom, we observe that a two-shell sampling scheme appears to be preferred for orientation estimation.

2. D. Kim, B. Zhao, L. L. Wald, J. P. Haldar.
Multidimensional T1 Relaxation-T2 Relaxation Correlation Spectroscopic Imaging with a Magnetic Resonance Fingerprinting Acquisition.
International Society for Magnetic Resonance in Medicine 27th Annual Meeting, Montreal, 2019, p. 4991. (abstract)

T1 Relaxation-T2 Relaxation Correlation Spectroscopic Imaging (RR-CSI) is a novel multidimensional imaging approach that estimates a 2D T1-T2 correlation spectrum at every spatial location, and enables spatial mapping of sub-voxel tissue compartments with very good compartmental resolving capabilities. While RR-CSI was previously demonstrated using data acquired with an inversion recovery multi-echo spin-echo sequence, it can also accommodate data acquired with other encoding schemes. In this work, we investigate an inversion recovery FISP MR fingerprinting acquisition scheme for RR-CSI. Results show, both theoretically and empirically using in vivo human data, that fingerprinting is a viable alternative.

3. T. H. Kim, P. Garg, J. P. Haldar.
LORAKI: Reconstruction of Undersampled k-space Data using Scan-Specific Autocalibrated Recurrent Neural Networks.
International Society for Magnetic Resonance in Medicine 27th Annual Meeting, Montreal, 2019, p. 4647. (abstract)

We introduce LORAKI, a novel MRI reconstruction method that bridges two powerful existing approaches (LORAKS and RAKI). Like RAKI (a deep learning extension of GRAPPA), LORAKI trains a scan-specific autocalibrated convolutional neural network (which only relies on autocalibration data, and does not require external training data) to interpolate missing k-space samples. However, unlike RAKI, LORAKI is based on a recurrent convolutional neural network architecture that is motivated by the iterated convolutional structure of a certain LORAKS algorithm. LORAKI is very flexible and can accommodate arbitrary k-space sampling patterns. Experimental results suggest LORAKI can have better reconstruction performance than state-of-the-art methods.

4. R. A. Lobos, J. P. Haldar.
Improving the Performance of Accelerated Image Reconstruction in K-Space: The Importance of Kernel Shape.
International Society for Magnetic Resonance in Medicine 27th Annual Meeting, Montreal, 2019, p. 2407. (abstract)

A variety of popular k-space reconstruction methods (e.g., GRAPPA, SPIRiT, SAKE, LORAKS) assume that missing k-space data can be interpolated by convolving the k-space data with appropriate filters. In most of these methods, the kernel shape is usually chosen to be rectangular. However, when these filters are interpreted in the spatial domain, the use of rectangular kernels implies that the filters will have anisotropic resolution. In this work, we investigate the use of elliptical kernels that have more isotropic resolution. Results demonstrate that elliptical kernels have better reconstruction performance, lower computational complexity, and lower memory usage than rectangular kernels.

5. Y. Liu, J. P. Haldar.
NAPALM: An Algorithm for MRI Reconstruction with Separate Magnitude and Phase Regularization.
International Society for Magnetic Resonance in Medicine 27th Annual Meeting, Montreal, 2019, p. 4764. (abstract)

We describe a new algorithm for model-based MRI reconstruction with separate magnitude and phase regularization. The algorithm, named NAPALM, combines the existing proximal alternating linearized minimization (PALM) algorithm for nonsmooth and nonconvex optimization with Nesterov's acceleration and adaptive gradient (AdaGrad) acceleration methods. Results demonstrate the advantages of NAPALM over existing state-of-the-art algorithms.

6. Y. Liu, C. Liao, K. Setsompop, J. P. Haldar.
Whole-brain DTI at 860 μm isotropic resolution in 10 minutes on a commercial 3T Scanner.
International Society for Magnetic Resonance in Medicine 27th Annual Meeting, Montreal, 2019, p. 3352. (abstract)

We describe an acquisition and reconstruction methodology that enables in vivo human diffusion tensor imaging with whole-brain coverage and 860μm isotropic spatial resolution, all within a 10 minute acquisition window on a commercial 3T scanner. Our approach is enabled by combining the gSlider-SMS acquisition approach (which uses simultaneous multi-slab acquisition for increased spatial coverage, combined with highly-efficient RF slab-encoding to achieve high spatial resolution) with an SNR-enhancing joint reconstruction approach that mitigates the noise associated with high-resolution acquisition.

7. F. Sepehrband, R. P. Cabeen, J. Jin, J. P. Haldar, A. W. Toga.
In-vivo diffusion imaging of hippocampal network with 600 μm isotropic resolution at 7T.
International Society for Magnetic Resonance in Medicine 27th Annual Meeting, Montreal, 2019, p. 996. (abstract)

Neuroimaging findings indicate that neurological disorders differentially target distinct subregions of the hippocampal circuit. Therefore, the ability to image hippocampal network is essential to study the mechanism of the disease pathophysiology. Here we propose a novel framework that enables high-resolution intra-hippocampal macro-structural and network diffusion imaging.

#### 2018

1. D. Kim, J. L. Wisnowski, C. T. Nguyen, J. P. Haldar.
Multidimensional T1 Relaxation-T2 Relaxation Correlation Spectroscopic Imaging (RR-CSI) for In Vivo Imaging of Microstructure.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 783. (abstract)
Recipient of a Summa Cum Laude ISMRM Merit Award.
Featured as one of the 'Science & Education Highlights' of the meeting (32 highlights were selected from 5,651 abstracts)

We propose a new multidimensional MRI experiment called T1 Relaxation-T2 Relaxation Correlation Spectroscopic Imaging (RR-CSI) for probing microstructure. RR-CSI acquires imaging data with two-dimensional relaxation contrast encoding and estimates a high-dimensional spectroscopic image by using spatially-constrained reconstruction. The spectroscopic image comprises a full 2D T1-T2 spectrum at every voxel. The distinct peaks in these spectra correspond to different microscopic tissue compartments, which enables spatial mapping of microstructure. Compared to conventional methods, RR-CSI has improved capabilities for resolving tissue microenvironments with similar relaxation parameters. RR-CSI is demonstrated with real MRI data, including the first in vivo human brain results.

2. T. H. Kim, J. P. Haldar.
Assessing MR image reconstruction quality using the Fourier Radial Error Spectrum plot.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 249. (abstract)

This work introduces the Fourier radial error spectrum plot (ESP) as a novel approach to quantifying the quality of reconstructed MR images. While conventional error metrics such as normalized root mean squared error (NRMSE) or structural similarity (SSIM) are widely used, they are simple scalar-measures that only provide one-dimensional insight into image quality. In contrast, ESP describes reconstruction quality with a spectrum that provides a quantitative evaluation of image quality at every spatial resolution scale. Our results show that ESP provides more comprehensive information than conventional error metrics, and can guide the design of new and improved image reconstruction approaches.

3. R. A. Lobos, A. Javed, K. S. Nayak, W. S. Hoge, J. P. Haldar.
Robust Autocalibrated LORAKS for Improved EPI Ghost Correction with Structured Low-Rank Matrix Models.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 3533. (abstract)

The presence of ghost artifacts is a recurrent problem in EPI images, which has been recently addressed using structured low-rank matrix (SLM) methods. In this work we propose a new SLM ghost correction method called Robust Autocalibrated LORAKS (RAC-LORAKS). RAC-LORAKS considers autocalibrated k-space constraints (similar to GRAPPA) to deal with the ill-posedness of existing SLM EPI ghost correction methods. RAC-LORAKS additionally adapts these constraints to enable robustness to possible imperfections in the autocalibration data. We illustrate the capabilities of RAC-LORAKS in two challenging scenarios: highly accelerated EPI of the brain, and cardiac EPI with double-oblique slice orientation.

4. D. Varadarajan, J. P. Haldar.
ERFO: Improved ODF estimation by combining machine learning with linear estimation theory.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 1557. (abstract)

Hiqh-quality diffusion tractography depends on the accurate estimation of orientation distribution functions (ODFs). Existing estimation methods often use modeling assumptions that are violated by real data, lack theoretical characterization, and/or are only applicable to a narrow class of q-space sampling patterns. As a result, existing approaches may be suboptimal. This work proposes a novel ODF estimation approach that learns a linear ODF estimator from training data. The approach can be applied to arbitrary q-space sampling schemes, has strong theoretical justification, and it can be shown that the trained estimators will generalize to new settings they weren't trained for.

5. B. Zhao, J. P. Haldar, C. Liao, D. Ma, M. A. Griswold, K. Setsompop, L. L. Wald.
Optimal experiment design for magnetic resonance fingerprinting: New insights and further improvements.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 674. (abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

The Cramer-Rao bound (CRB) based experiment design was previously described to optimize the SNR efficiency of MRF experiments. Here we revisit such a problem and provide new insights. Specifically, we present a new CRB-based experiment design approach, which introduces an additional set of constraints on the variation of flip angles to enforce the smoothness of the magnetization evolution. We demonstrate that the proposed approach is advantageous for highly-undersampled MRF experiments. We evaluated the effectiveness of the proposed approach with both simulations and phantom experiments.

6. B. Zhao, B. Gagoski, J. P. Haldar, E. Adalsteinsson, E. Grant, L. L. Wald.
A subspace approach to accelerated HASTE acquisition for fetal brain MRI.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 2450. (abstract)

HAlf-fourier Single-shot Turbo spin Echo (HASTE) acquisition is widely used in fetal MR imaging due to its T2 contrast and motion robustness, but speed and T2-blurring remain a problem for fully sampled acquisitions. In the work, we describe a new reconstruction approach based on low-rank and subspace modeling of local k-space neighborhood to accelerate HASTE acquisition. The proposed approach decreases the echo-train length with improved image quality and noise robustness compared to conventional reconstruction. It is compatible with the vendor-provided acquisition. The effectiveness and utility of the proposed approach is evaluated with both retrospectively and prospectively undersampled fetal imaging data.

7. B. Bilgic, T. H. Kim, C. Liao, M. K. Manhard, L. L. Wald, J. P. Haldar, K. Setsompop.
Improving parallel imaging by jointly reconstructing multi-contrast data.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 3505. (abstract)

We propose a general joint reconstruction framework to accelerate multi-contrast acquisitions further than currently possible with conventional parallel imaging. Our joint parallel imaging techniques simultaneously exploit similarities between echoes/phase-cycles/contrasts, virtual coil concept, partial Fourier acquisition, complementary sampling across images along with limited support and smooth phase constraints. These permit highly accelerated 2D, Simultaneous MultiSlice and 3D acquisitions as well as improved calibrationless parallel imaging from multiple contrasts. Our algorithms, JVC-GRAPPA and J-LORAKS, provide over 2-fold improvement in reconstruction error compared to conventional GRAPPA, with improved mitigation of artifacts and noise amplification.

8. Y. Bliesener, S. G. Lingala, J. P. Haldar, K. S. Nayak.
Influence of whole-brain DCE-MRI (k,t) sampling strategies on variance of pharmaco-kinetic parameter estimates.
Joint Annual Meeting ISMRM-ESMRMB, Paris, 2018, p. 555. (abstract)
Featured with a Power Pitch presentation (hand-selected as one of the 330 most interesting abstracts out of 5,651 accepted).

We investigate the influence of 2D (ky,kz,t) sampling strategies on the minimum achievable variance without bias for pharmaco-kinetic parameter estimation in 3D whole-brain DCE-MRI (equivalent to the best possible precision without bias). Cramer-Rao analysis is combined with a pathologically- and anatomically-realistic digital reference object to objectively compare measurement procedures independent of any estimator. This study did not identify any significant difference between lattice and random undersampling, or between their uniform and variable density variants.

9. D. Kim, J. L. Wisnowski, C. T. Nguyen, J. P. Haldar.
Probing in vivo microstructure with T1-T2 relaxation correlation spectroscopic imaging.
IEEE International Symposium on Biomedical Imaging, Washington, DC, 2018, p. 675-678.
PubMed Central ID: PMC6405227.

Quantitative MR relaxometry can provide unique subvoxel information about the microscopic tissue compartments that are present in a large imaging voxel. However, unambiguously distinguishing between these tissue compartments continues to be challenging with conventional methods due to the ill-posedness of the inverse problem. This paper describes a new imaging approach, which we call T1 Relaxation-T2 Relaxation Correlation Spectroscopic Imaging (RR-CSI), that uses two-dimensional relaxation encoding combined with spatially-constrained reconstruction to help overcome ill-posedness. Results are shown with real data, including what we believe to be the first in vivo demonstration of multidimensional relaxation correlation spectroscopic imaging.

10. D. Varadarajan, J. P. Haldar.
Towards optimal linear estimation of orientation distribution functions with arbitrarily sampled diffusion MRI data.
IEEE International Symposium on Biomedical Imaging, Washington, DC, 2018, p. 743-746.
PubMed Central ID: PMC6448790.

The estimation of orientation distribution functions (ODFs) from diffusion MRI data is an important step in diffusion tractography, but existing estimation methods often depend on signal modeling assumptions that are violated by real data, lack theoretical characterization, and/or are only applicable to a small range of q-space sampling patterns. As a result, existing ODF estimation methods may be suboptimal. In this work, we propose a novel ODF estimation approach that learns a linear ODF estimator from training data. The training set contains ideal data samples paired with corresponding ideal ODFs, and the learning procedure reduces to a simple linear least-squares problem. This approach can accommodate arbitrary q-space sampling schemes, can be characterized theoretically, and is theoretically demonstrated to generalize far beyond the training set. The proposed approach is evaluated with simulated and in vivo diffusion data, where it is demonstrated to outperform common alternatives.

11. R. A. Lobos, A. Javed, K. S. Nayak, W. S. Hoge, J. P. Haldar.
Robust Autocalibrated LORAKS for EPI Ghost Correction.
IEEE International Symposium on Biomedical Imaging, Washington, DC, 2018, p. 663-666.
PubMed Central ID: PMC6461404.

Nyquist ghosts are a longstanding problem in a variety of fast MRI experiments that use echo-planar imaging (EPI). Recently, several structured low-rank matrix modeling approaches have been proposed that achieve state-of-the-art ghost-elimination, although the performance of these approaches is still inadequate in several important scenarios. We present a new structured low-rank matrix recovery ghost correction method that we call Robust Autocalibrated LORAKS (RAC-LORAKS). RAC-LORAKS incorporates constraints from autocalibration data to avoid ill-posedness, but allows adaptation of these constraints to gain robustness against possible autocalibration imperfections. RAC-LORAKS is tested in two challenging scenarios: highly-undersampled multi-channel EPI of the brain, and cardiac EPI with a double-oblique slice orientation. Results show that RAC-LORAKS can provide substantial improvements over existing ghost correction methods, and potentially enables new imaging applications that were previously confounded by ghost artifacts.

12. T. H. Kim, J. P. Haldar.
The Fourier Radial Error Spectrum Plot: A more nuanced quantitative evaluation of image reconstruction quality.
IEEE International Symposium on Biomedical Imaging, Washington, DC, 2018, p. 61-64.
PubMed Central ID: PMC6472927.

In the modern biomedical image reconstruction literature, the quality of a reconstructed image is often numerically quantified using scalar error measures such as mean-squared error or the structural similarity index. While such measures provide a rough summary of image quality, they also suffer from well-known limitations. For example, a substantial amount of information is necessarily lost whenever the characteristics of a high-dimensional image are summarized by a single number. In this work, we introduce the Fourier radial Error Spectrum Plot (ESP), which provides a novel and more nuanced assessment of error by decomposing the error into its different spatial frequency components. The usefulness of ESP is illustrated in the context of MRI reconstruction from under-sampled data. In addition, we demonstrate that the extra dimension of insight provided by ESP can be used to improve the performance of existing image reconstruction techniques.

#### 2017

1. B. Kim, D. B. Kay, N. Schweighofer, J. P. Haldar, R. M. Leahy, S. Choi, B. Fisher, C. J. Winstein.
Quantification of corticospinal tract using DTI in chronic stroke survivors.
Society for Neuroscience 47th Annual Meeting, Washington, DC, 2017, p. 306.13. (Abstract)

There are a number of different DTI-based methods that have been used to quantify corticospinal tract (CST) structure in the context of stroke rehabilitation research. However, there is no gold standard method that has been shown to provide the most accurate estimate of CST structure in chronic stroke survivors. This study aims to compare different DTI-based approaches to quantify CST structural characteristics in chronic stroke survivors, and to determine which, if any, reveals the strongest brain-behavior relationship. We used DTI and clinical motor behavior data from a phase-I clinical trial. Participants were chronic stroke survivors with mild-tomoderate arm and hand motor impairment (N=37, average chronicity=3 years). We processed the Imaging data using BrainSuite16a (http://brainsuite.org/), and used the Wolf Motor Function Test log mean time score for distal control items (WMFT-distal) as the primary motor behavior measure. We calculated mean Fractional Anisotropy (FA) for CST of each tract (L, R) with 7 different approaches: 1) manually drawn 2-D posterior limb of the internal capsule (PLIC) region, 2) manually drawn 2-D cerebral peduncle (CP) region, 3) 3-D PLIC template volume from a JHU white matter atlas, 4) 3-D CP template volume from a JHU white matter atlas, 5) 3-D CST individual volume from each participant's tractography, 6) 3-D CST template volume from a standard white matter atlas, and 7) 3-D CST template volume generated from participants' contra-lesional CST. We compared CST FA between the two tracts for each method using a paired t-test; calculated a CST FA asymmetry index between the two hemispheres from each approach, and performed partial correlation analyses between each CST FA asymmetry index and WMFT-distal time score, controlled for age, chronicity, and severity. The mean ipsilesional CST FA was significantly lower than the mean contralesional CST FA for all 7 methods. Only CST FA asymmetry from the 3-D CST individual volume from each participant's tractography significantly correlated with WMFT-distal (r=0.46, p=0.005). Further only range of CST FA asymmetry from individual tractography met the criterion of CST FA asymmetry for those who have mild-to-moderate arm motor impairment. These findings suggest that compared to the six other methods, CST FA asymmetry based on the individual's CST tractography is the most accurate estimate of CST structural characteristics in chronic stroke survivors with mild-to-moderate motor impairment. We recommend this method for future studies in chronic stroke that aims to investigate the relationship between CST structural characteristics and motor behavior.

2. D. Kim, J. L. Wisnowski, J. P. Haldar.
Improved Efficiency for Microstructure Imaging using High-Dimensional MR Correlation Spectroscopic Imaging.
Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, 2017, p. 1264-1268.
Invited Presentation.

Magnetic Resonance Correlation Spectroscopic Imaging (MR-CSI) is a high-dimensional imaging approach that our group recently introduced for studying microstructure. MR-CSI uses imaging data that is simultaneously encoded with multiple MR contrast mechanisms, and applies a spatial-spectral reconstruction framework to estimate a spectroscopic image with a high-dimensional correlation spectrum for every spatial location. While MR-CSI enables powerful new capabilities for spatially mapping sub-voxel microstructural compartments, the contrast encoding can be slow due to the curse of dimensionality. This paper reviews MR-CSI and investigates a principled estimation theoretic approach that can enable more efficient experiment designs.

3. J. P. Haldar, T. H. Kim.
Computational imaging with LORAKS: Reconstructing linearly predictable signals using low-rank matrix regularization.
Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, 2017, p. 1870-1874.
Invited Presentation.

Although many modern computational imaging approaches use sparse or low-rank modeling constraints, it should not be forgotten that many classical computational imaging approaches rely on a different kind of constraint: linear predictability. Several years ago, we introduced the LORAKS framework, which combines classical linear prediction models with modern low-rank matrix completion approaches. LORAKS makes the observation that linear prediction assumptions can be embedded into high-dimensional structured low-rank matrix constraints. This enables a powerful and flexible new approach for modeling and reconstructing images. In this work, we review LORAKS and describe our recent progress.

4. D. Kim, J. L. Wisnowski, J. P. Haldar.
MR correlation spectroscopic imaging of multidimensional exponential decays: probing microstructure with diffusion and relaxation.
Wavelets and Sparsity XVII, Proceedings of SPIE 10394, San Diego, 2017, p. 103940D.
Invited Presentation.

Diffusion-relaxation correlation spectroscopic imaging (DR-CSI) is a novel multidimensional magnetic resonance (MR) imaging approach that we recently introduced for probing microstructure. DR-CSI uses high-dimensional MR data that is acquired with spatial encoding and non-separable diffusion-relaxation contrast encoding, and uses constrained image reconstruction to estimate a spectroscopic image with a multidimensional spectrum for each voxel. The spectral peaks correspond to distinct compartmental microenvironments that coexist within each voxel. This paper reviews DR-CSI and describes and demonstrates its generalization to other contrast mechanisms (i.e., we demonstrate multidimensional relaxation (T1-T2) correlation spectroscopic imaging).

5. D. Varadarajan, J. P. Haldar.
Theoretical characterization of angular resolution for linear ODF estimation.
23rd Annual Meeting of the Organization for Human Brain Mapping, Vancouver, 2017, p. 1747. (Abstract)

6. J. P. Haldar, D. Kim.
OEDIPUS: Towards optimal deterministic k-space sampling for sparsity-constrained MRI.
International Society for Magnetic Resonance in Medicine 25th Annual Meeting, Honolulu, 2017, p. 3877. (Abstract)

We propose a novel approach to designing optimal k-space sampling patterns for sparsity-constrained MRI. The new approach, called OEDIPUS (Oracle-based Experiment Design for Imaging Parsimoniously Under Sparsity constraints), is inspired by insights and methods from estimation theory and the statistical design of experiments. Specifically, OEDIPUS combines the oracle-based Cramér-Rao bound for sparsity-constrained reconstruction with sequential greedy algorithms for observation selection. We demonstrate that OEDIPUS can be used to deterministically and automatically generate k-space sampling patterns that are tailored to specific hardware and application contexts, and which lead to better reconstruction performance relative to conventional sampling approaches for sparse MRI.

7. J. P. Haldar, K. Setsompop.
Fast high-resolution diffusion MRI using gSlider-SMS, interlaced subsampling, and SNR-enhancing joint reconstruction.
International Society for Magnetic Resonance in Medicine 25th Annual Meeting, Honolulu, 2017, p. 175. (Abstract)

We describe a new approach that enables in vivo whole brain diffusion MRI with simultaneously high spatial resolution (660 μm isotropic voxels) and high angular diffusion encoding resolution (64 orientations at b=1500 s/mm2 and 4 b=0 s/mm2 images) in only 15 minutes. This is achieved by combining the gSlider-SMS acquisition strategy with constrained image reconstruction techniques that enable denoising (exploiting the fact that the diffusion images are smooth with correlated edge locations) and interlaced data subsampling (achieved by exploiting the same correlated edge constraints used for denoising, as well as through the use of q-space smoothness constraints).

8. D. Kim, J. P. Haldar.
Faster Diffusion-Relaxation Correlation Spectroscopic Imaging (DR-CSI) using Optimized Experiment Design.
International Society for Magnetic Resonance in Medicine 25th Annual Meeting, Honolulu, 2017, p. 176. (Abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

We propose a new experiment design method to accelerate the recent novel diffusion-relaxation correlation spectroscopic imaging (DR-CSI) experiment. DR-CSI acquires imaging data across a range of different b-value and echo time combinations. This enables new insights into tissue microstructure, but the contrast encoding can be slow. Our experiment design approach selects a small subset of the most informative observations to acquire using results from estimation theory. We demonstrate with ex vivo mouse spinal cord MR data that the new experiment design approach enables DR-CSI to be accelerated by a factor of more than 2 without a substantial loss in quality.

9. D. Kim, E. K. Doyle, J. L. Wisnowski, J. P. Haldar.
Phantom Validation of Diffusion-Relaxation Correlation Spectroscopic Imaging (DR-CSI).
International Society for Magnetic Resonance in Medicine 25th Annual Meeting, Honolulu, 2017, p. 609. (Abstract)
Recipient of the 1st Place Award for Best Abstract Presentation from the ISMRM Quantitative MR Study Group.

Diffusion-relaxation correlation spectroscopic imaging (DR-CSI) is a novel multidimensional MR imaging approach that infers microscopic tissue compartments using simultaneous diffusion and relaxation information. The approach was previously demonstrated with biological data, although validation was not possible in the absence of a gold standard reference. In this work, we perform simulation and experimental studies, using a gold standard for validation. Specifically, we custom-built a multi-compartment diffusion-relaxation phantom with known characteristics, and performed extensive comparisons between DR-CSI and conventional multi-compartment estimation methods. Our results demonstrate that DR-CSI has good performance, enabled by the combination of multidimensional encoding and constrained spectroscopic image reconstruction.

10. T. H. Kim, B. Bilgic, D. Polak, K. Setsompop, J. P. Haldar.
Wave-LORAKS for faster Wave-CAIPI MRI.
International Society for Magnetic Resonance in Medicine 25th Annual Meeting, Honolulu, 2017, p. 1037. (Abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

Wave-CAIPI is a novel technique that enables accelerated acquisition with negligible g-factor penalty by using corkscrew readout trajectories, while LORAKS (LOw-RAnk modeling of local K-Space neighborhoods) is a powerful approach to constrained reconstruction that integrates sparse support, phase, and parallel imaging constraints into a unified linear prediction framework. In this work, we propose a new fast imaging technique called Wave-LORAKS, which combines Wave-CAIPI acquisition with LORAKS-based reconstruction. Retrospective undersampling experiments with 3D T1-weighted data show that Wave-LORAKS enables higher acceleration and more flexible sampling compared to traditional Wave-CAIPI, allowing up to 15-fold acceleration with similar quality as 9-fold accelerated Wave-CAIPI.

11. R. A. Lobos, T. H. Kim, W. S. Hoge, J. P. Haldar.
Navigator-free EPI ghost correction using low-rank matrix modeling: Theoretical insights and practical improvements.
International Society for Magnetic Resonance in Medicine 25th Annual Meeting, Honolulu, 2017, p. 449. (Abstract)
Recipient of a Summa Cum Laude ISMRM Merit Award.
Featured with a Power Pitch presentation (hand-selected as one of the 220 most interesting abstracts out of 6,780 submissions to the conference).

While the formation of ghost-free images from EPI data can be a difficult problem, recent low-rank matrix modeling methods have demonstrated promising results. In this abstract, we provide new theoretical insight into these approaches, and show that the low-rank ghost correction optimization problem has infinitely many solutions without using additional constraints. However, we also show that SENSE-like or GRAPPA-like constraints can be successfully used to make the problem well-posed, even for single-channel data. Additionally, we show that substantial performance gains can be achieved over previous low-rank ghost correction implementations by using nonconvex low-rank regularization instead of previous convex approaches.

12. Y. Bliesener, S. G. Lingala, J. P. Haldar, K. S. Nayak.
Comparison of (k,t) sampling schemes for DCE MRI pharmacokinetic parameter estimation.
International Society for Magnetic Resonance in Medicine 25th Annual Meeting, Honolulu, 2017, p. 1909. (Abstract)

We demonstrate an approach to evaluate and compare (k,t) sampling patterns for DCE-MRI. We compute Cramér-Rao lower bounds on the variance of pharmacokinetic (PK) parameter estimates, using pathologically- and anatomically-realistic digital reference objects. The framework allows for the optimization of sampling patterns independent of any specific estimator. We apply this framework to a 2D reference object for four sampling patterns: keyhole, TRICKS, lattice, and golden angle sampling. It is shown that TRICKS, lattice, and golden angle sampling enable low variance estimation for low undersampling factors. Out of these, lattice sampling keeps variances lowest with increasing undersampling factors.

#### 2016

1. B. Kim, D. B. Kay, N. Schweighofer, J. P. Haldar, R. M. Leahy, B. Fisher, C. J. Winstein.
Changes in corticospinal tract microstructure are associated with motor performance improvement in chronic stroke.
Society for Neuroscience 46th Annual Meeting, San Diego, 2016, p. 520.26. (Abstract)

Background: Microstructure of corticospinal tract (CST) characterized by diffusion tensor imaging (DTI) has been shown to be a significant predictor of motor recovery after stroke in both acute and chronic stroke. While CST microstructural change during the early phase has been shown to be associated with motor recovery, there is no study showing a significant relationship between the change in CST microstructure and the change in motor performance in chronic stroke. Purpose: This study aims to determine if a change in ipsilesional CST (iCST) fractional anisotropy (FA) is associated with improvement in paretic upper extremity (UE) motor performance over a three-month intervention period. These data are a subset of a longitudinal Phase-I clinical trial of rehabilitation in chronic stroke (ClinicalTrials.gov ID: NCT01749358). Methods: Those with mild-to-moderate UE motor impairment participated (N=28, chronicity range = 0.47 to 14.38 years). MRI scans and clinical assessments were acquired at baseline and post a 3-month period. Imaging data were processed using BrainSuite14a (http://brainsuite.org/). CST tractography was reconstructed for both ipsi- and contra-lesional sides, and 3-dimensional CST masks were generated for each side. Average FA values of each voxel within CST mask was calculated for each side, and CST FA asymmetry index (FAAI) was derived. The primary motor outcome was average Wolf Motor Function Test (WMFT) log time score of distal control items. Significant changes in DTI and motor performance variables were assessed using repeated measures ANOVA. Relationship between change in DTI variables and change in motor performance was assessed using linear regression. Results: There was a significant decrease in WMFT log time score over a 3-month period (mean ± standard deviation of changes = -8.4 ± 10.8 %, p < 0.05). Changes in the iCST FA and FAAI were not significant (p = 0.82 and p = 0.15, respectively). However, the linear regression revealed that changes in iCST FA and FAAI explained 35 % (p < 0.0001) and 33% (p < 0.01) of the variance in change in log time score of WMFT distal items, respectively. Discussion: This is the first study in a chronic stroke population that has demonstrated a significant relationship between CST microstructural change and motor performance improvement. However, we did not set covariates in the linear regression, such as age and chronicity that can affect FA value, due to the small sample size. We need more studies with larger sample size to develop a better model for the relationship between brain microstructure and motor behavior.

2. B. Zhao, J. P. Haldar, K. Setsompop, L. L. Wald.
Optimal Experiment Design for Magnetic Resonance Fingerprinting.
38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Orlando, 2016, pp. 453-456.

Magnetic resonance (MR) fingerprinting is an emerging quantitative MR imaging technique that simultaneously acquires multiple tissue parameters in an efficient experiment. In this work, we present an estimation-theoretic framework to evaluate and design MR fingerprinting experiments. More specifically, we derive the Cramer-Rao bound (CRB), a lower bound on the covariance of any unbiased estimator, to characterize parameter estimation for MR fingerprinting. We then formulate an optimal experiment design problem based on the CRB to choose a set of acquisition parameters (e.g., flip angles and/or repetition times) that maximizes the signal-to-noise ratio efficiency of the resulting experiment. The utility of the proposed approach is validated by numerical studies. Representative results demonstrate that the optimized experiments allow for substantial reduction in the length of an MR fingerprinting acquisition, and substantial improvement in parameter estimation performance.

3. M. Chong, C. Bhushan, A. Joshi, J. Haldar, R. N. Spreng, R. Leahy.
Individual Performance of Resting fMRI Parcellation with Group Connectivity Priors.
22nd Annual Meeting of the Organization for Human Brain Mapping, Geneva, 2016, p. 2214. (Abstract)

4. C. Bhushan, M. Chong, S. Choi, A. Joshi, J. Haldar, H. Damasio, R. Leahy.
Non-local means filtering for cortical parcellation of resting fMRI.
22nd Annual Meeting of the Organization for Human Brain Mapping, Geneva, 2016. (Abstract)

5. J. P. Haldar, Q. Fan, K. Setsompop.
Whole-brain quantitative diffusion MRI at 660 μm resolution in 25 minutes using gSlider-SMS and SNR-enhancing joint reconstruction.
International Society for Magnetic Resonance in Medicine 24th Annual Meeting, Singapore, 2016, p. 102. (Abstract)
Featured with a Power Pitch presentation (hand-selected as one of the 165 most interesting abstracts out of 5,915 submissions to the conference).

We propose a novel approach to data acquisition and image reconstruction that achieves high-quality in vivo whole-brain human diffusion imaging at (660 μm)3 resolution in 25 minutes. The approach uses a powerful acquisition strategy (generalized SLIce Dithered Enhanced Resolution Simultaneous MultiSlice, or gSlider-SMS) that enables high-resolution whole-brain imaging in 25 minutes (64 diffusion weightings + 7 b=0 images), but the resulting images suffer from low SNR without averaging. To address the SNR problem, we utilize a regularized reconstruction/denoising approach that leverages the shared spatial structure of different diffusion images. In vivo results demonstrate the effectiveness of this approach.

6. D. Kim, J. H. Kim, J. P. Haldar.
Diffusion-Relaxation Correlation Spectroscopic Imaging (DR-CSI): An Enhanced Approach to Imaging Microstructure.
International Society for Magnetic Resonance in Medicine 24th Annual Meeting, Singapore, 2016, p. 660. (Abstract)
One of the top ten most popular abstracts of the meeting (out of 5,915 submissions).

We propose a new MR experiment called diffusion-relaxation correlation spectroscopic imaging (DR-CSI). DR-CSI acquires imaging data across a range of different b-value and echo time combinations, and then performs regularized reconstruction to generate a 2D diffusion-relaxation correlation spectrum for every voxel. The peaks of this spectrum correspond to the different tissue microenvironments that are present within each macroscopic imaging voxel, which provides powerful insight into the tissue microstructure. Compared to standard relaxometry or diffusion imaging, DR-CSI provides unique capabilities to resolve tissue compartments that have similar relaxation or diffusion parameters. DR-CSI is demonstrated with spinal cord traumatic injury MRI data.

7. T. H. Kim, K. Setsompop, J. P. Haldar.
SENSE-LORAKS: Phase-Constrained Parallel MRI without Phase Calibration.
International Society for Magnetic Resonance in Medicine 24th Annual Meeting, Singapore, 2016, p. 1089. (Abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

We introduce a novel framework called SENSE-LORAKS for partial Fourier phase-constrained parallel MRI reconstruction. SENSE-LORAKS combines classical SENSE data modeling with advanced regularization based on the novel low-rank modeling of local k-space neighorhoods (LORAKS) framework. Unlike conventional phase-constrained SENSE techniques, SENSE-LORAKS enables use of phase constraints without requiring a prior estimate of the image phase or a fully sampled region of k-space that could be used for phase autocalibration. Compared to previous SENSE-based and LORAKS-based reconstruction approaches, SENSE-LORAKS is compatible with a much wider range of sampling trajectories, which can be leveraged to achieve much higher acceleration rates.

8. D. Varadarajan, J. P. Haldar.
A Theoretical Framework for Sampling and Reconstructing Ensemble Average Propagators in Diffusion MRI.
International Society for Magnetic Resonance in Medicine 24th Annual Meeting, Singapore, 2016, p. 2049. (Abstract)

Diffusion MRI can be modeled as sampling the Fourier transform of the Ensemble Average Propagator (EAP). This is potentially advantageous because of extensive theory that has been developed to characterize sampling requirements, accuracy, and stability for Fourier reconstruction. However, previous work has not taken advantage of this characterization. This work presents a novel theoretical framework that precisely describes the relationship between the estimated EAP and the true original EAP. The framework is applicable to arbitrary linear EAP estimation methods, and for example, provides new insights into the design of q-space sampling patterns and the selection of EAP estimation methods.

9. B. Zhao, J. P. Haldar, K. Setsompop, L. L. Wald.
Towards Optimized Experiment Design for Magnetic Resonance Fingerprinting.
International Society for Magnetic Resonance in Medicine 24th Annual Meeting, Singapore, 2016, p. 2835. (Abstract)

A principled framework is proposed to optimize the experiment design for magnetic resonance fingerprinting (MRF) based on the Cramer-Rao bound. Within this framework, we optimize the acquisition parameters (flip angle, TR, etc.) to maximize the SNR efficiency of quantitative parameter estimation. Preliminary results indicate that the optimized experiments allow for substantially reducing the length of an MRF acquisition and substantially improving estimation performance for the T2 map, while maintaining similar accuracy level for the T1 map. The proposed framework should prove useful for fast quantitative MR imaging with MRF.

10. T. H. Kim, K. Setsompop, J. P. Haldar.
Partial Fourier SENSE Reconstruction without Phase Calibration.
ISMRM Workshop on Data Sampling & Image Reconstruction, Sedona, 2016. (Abstract)

#### 2015

1. B. Kim, Y. Oh, R. M. Leahy, J. P. Haldar, N. Schweighofer, C. J. Winstein.
Is structural connectivity of basal ganglia associated with learned non-use in chronic stroke?
American Society of Neurorehabilitation Annual Meeting, Chicago, 2015. (Abstract)
[toggle abstract]

In those with mild to moderate stroke impairment, there can be a discrepancy between movement capability and daily use of the affected arm and hand. This is captured by the phrase, "he can, but does he?" This phenomenon may be a consequence of negative reinforcement resulting from affected arm use and positive reinforcement for less-affected arm use. The basal ganglia (BG), especially ventral striatum, are considered the neural reward center for reinforcement learning. Thus, the BG may have an important role in mediating the learned non-use phenomenon in chronic stroke. The primary aim is to investigate whether the structural connectivity of BG to other sensorimotor brain areas is associated with affected arm use. This study is part of a larger longitudinal Phase-I clinical trial of rehabilitation in chronic stroke (ClinicalTrials.gov ID: NCT 01749358). Individuals with mild to moderate motor impairment after stroke participated (N=24, average chronicity= 3.04 years). Structural brain images (T1-weighted MRI and DTI) were acquired, and processed using BrainSuite14a (http://brainsuite.org/). A total of twenty-four cortical or subcortical sensorimotor areas (Twelve regions of interests [ROIs] in each hemisphere) and a cerebellum ROI were chosen to construct a structural network. We calculated the Fractional anisotropy (FA) of each tractography between each ROI pair. A 25 X 25 FA matrix was generated to produce an undirected weighted graph. A weighted communicability graph was also computed from the raw FA matrix. Network metrics, including strength and degree, were calculated from FA and communicability graphs for each ROI. We calculated an asymmetric index (AI) of each network metric between an ROI and its homologous ROI in the other hemisphere. Motor Activity Log (MAL) was used to quantify the paretic arm use in daily activities. Linear regression analyses were used to test the relationship between connectivity metrics and MAL score. Significance level was set using Bonferroni correction for multipe comparisons (alpha=0.05/12=0.00417). There was no significant linear relationship between any network metrics and MAL score. However, the communicability strength AI (CSAI) of caudate nucleus showed the highest effect size on the MAL score among twelve CSAIs. 17% of variance in MAL score was explained by the caudate CSAI (p=0.024, Effect size [Cohen's f 2 ] = 0.21). Other ROIs' CSAI had smaller effect size than caudate CSAI on the MAL score (Cohen's f 2 < 0.10). This result provides partial support for our hypothesis that structural connectivity of BG is associated with affected arm use in chronic stroke. People with a higher caudate CSAI demonstrated less use of the affected arm in daily activities than those with a lower caudate CSAI. Future work should test whether a reduced structural connectivity of ipsilesional caudate nuclei is predictive of learned non-use, or is simply the result of affected arm non-use.

2. B. Kim, Y. Oh, R. M. Leahy, J. P. Haldar, N. Schweighofer, C. J. Winstein.
Brain sensorimotor structural network difference between two hemispheres in chronic stroke.
Society for Neuroscience 45th Annual Meeting, Chicago, 2015. (Abstract)

Brain network among sensorimotor areas in both hemispheres is affected by hemispheric stroke. Brain structural network analysis was introduced to identify adaptive changes across the brain network after cerebral stroke, and to understand the relationship between changes in the network and motor behavior. This study aims to determine whether brain sensorimotor structural network analysis can be used to investigate the relationship between brain sensorimotor networks and motor behavior. This study is part of a longitudinal Phase-I clinical trial of rehabilitation in chronic stroke (ClinicalTrials.gov ID: NCT 01749358). Individuals with mild to moderate motor impairment after stroke participated (N=24, average chronicity= 3.04 years). Structural brain images (T1-weighted MRI and DTI) were acquired. Imaging data were processed using BrainSuite14a (http://brainsuite.org/). A total of twenty four cortical or subcortical sensorimotor areas (Twelve areas in each hemisphere) were chosen to construct a structural connectivity network. Fractional anisotropy (FA) of the pathway (tractography between each pair of regions of interest [ROIs]) was calculated and a 24 X 24 FA matrix generated. We applied a threshold, optimized for each patient, to produce an undirected weighted graph and a binary adjacency matrix. Communicability between each pair of ROIs was calculated. Wolf Motor Function Test (WMFT) and Motor Activity Log (MAL) were performed to assess motor performance and the amount of the paretic arm use, respectively. For each ROI, the mean communicability was calculated, and a Wilcoxon signed-rank test was performed to compare the mean communicability between the homologous ROIs in the two hemispheres. Finally, Pearson correlation analysis was used to determine if there is a relationship between the brain sensorimotor network (communicability asymmetric index of each ROI and motor behavior (WMFT, MAL). The significance level was 0.05, and Bonferroni correction was applied for the Pearson correlation (alpha = 0.05/24 = 0.002). There was significantly lower communicability in ipsilesional superior parietal gyrus, caudate nucleus, putamen, and globus pallidus compared to communicability metrics of these same ROIs in contralesional hemisphere. However, any communicability metric was not significantly correlated with WMFT Time score or MAL score. These results show the potential use of sensorimotor tracts FA metrics to capture the brain sensorimotor structural network difference between two hemispheres in chronic stroke, although the asymmetry in communicability between hemispheres was not associated with the level of motor deficits.

3. V. L. Landes, T. H. Kim, J. P. Haldar, K. S. Nayak.
Experimental Validation of SMS-LORAKS.
ISMRM Workshop on Simultaneous Multi-Slice Imaging: Neuroscience & Clinical Applications, Pacific Grove, 2015. (Abstract)

4. M. Chong, A. Joshi, J. Haldar, E. DuPre, W.-M. Luh, D. Shattuck, R. N. Spreng, R. Leahy.
A Group Approach to Functional Cortical Parcellation from Resting-State fMRI.
21st Annual Meeting of the Organization for Human Brain Mapping, Honolulu, 2015, p. 3778. (Abstract)

5. J. P. Haldar.
Low-Rank Modeling of Local k-Space Neighborhoods: From Phase and Support Constraints to Structured Sparsity.
Wavelets and Sparsity XVI, Proceedings of SPIE 9597, San Diego, 2015, p. 959710.
Invited Presentation.

Low-rank modeling of local k-space neighborhoods (LORAKS) is a recent novel framework for constrained MRI reconstruction. LORAKS relies on embedding MRI data into carefully-constructed matrices, which will have low-rank structure when the MRI image has sparse support or slowly-varying phase. Low-rank matrix representation allows MRI images to be reconstructed from undersampled data using modern low-rank matrix techniques, and enables data acquisition strategies that are incompatible with more traditional representations. This paper reviews LORAKS, and describes extensions that allow LORAKS to additionally impose structured transform-domain sparsity constraints (e.g., structured sparsity of the image derivatives or wavelet coefficients).

6. J. P. Haldar.
AC-LORAKS: Autocalibrated Low-Rank Modeling of Local k-Space Neighborhoods.
International Society for Magnetic Resonance in Medicine 23rd Annual Meeting, Toronto, 2015, p. 2430. (Abstract)

Low-rank modeling of local k-space neighborhoods (LORAKS) is a recent framework for constrained MRI. While LORAKS is powerful, flexible, and enables the simultaneous use of support, phase, and parallel imaging constraints, previous implementations depended on the use of time-consuming low-rank matrix completion algorithms. In this work, we show that fast LORAKS reconstructions are possible if the sampling scheme contains an autocalibration region. Results are shown with real data to demonstrate the advantages of the proposed approach relative to previous LORAKS methods. The approach can also be used as a powerful alternative to autocalibrated parallel imaging methods like SPIRiT and PRUNO.

7. D. Kim, J. H. Kim, J. P. Haldar.
Automatic Tissue Decomposition using Nonnegative Matrix Factorization for Noisy MR Magnitude Images.
International Society for Magnetic Resonance in Medicine 23rd Annual Meeting, Toronto, 2015, p. 3701. (Abstract)

This work proposes a novel data-driven method for automatically decomposing a multi-contrast MRI dataset into a mixture of constituent spatially-overlapping tissue components. The approach is non-parametric (no physical models are necessary), instead relying on a combination of low-rank matrix modeling, sparsity, and nonnegativity constraints through the nonnegative matrix factorization (NMF) framework. We demonstrate that NMF, when combined with an appropriate non-central chi noise model, can be used to automatically decompose diffusion and relaxation MRI datasets, yielding partial volume maps of white matter, gray matter, cerebrospinal fluid, and abnormal/injured tissue components.

8. T. H. Kim, J. P. Haldar.
Simultaneous Multi-slice MRI Reconstruction using LORAKS.
International Society for Magnetic Resonance in Medicine 23rd Annual Meeting, Toronto, 2015, p. 78. (Abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

This work proposes a novel approach to simultaneous multi-slice (SMS) parallel MRI reconstruction, based on the low-rank modeling of local k-space neighborhoods (LORAKS) framework. Compared to existing SMS reconstruction methods, the proposed SMS-LORAKS approach is flexible enough to reconstruct highly-undersampled SMS data in the absence of prior coil information or autocalibration data. SMS-LORAKS can also be applied to single-channel MRI data. Reconstruction results are shown with real retrospectively-undersampled MRI data to demonstrate the potential of the approach.

9. D. Varadarajan, J. P. Haldar.
A New Linear Transform Approach for Estimating ODFs from Multi-Shell Diffusion Data.
International Society for Magnetic Resonance in Medicine 23rd Annual Meeting, Toronto, 2015, p. 2816. (Abstract)

The Funk-Radon and Cosine Transform (FRACT) is a recent linear method for estimating orientation distribution functions (ODFs) from single-shell diffusion MRI data. Compared to previous single-shell ODF estimation techniques, the FRACT offers predictable performance, strong theoretical characterization, and does not require any tissue modeling assumptions (that can confound nonlinear ODF estimation methods when the modeling assumptions are violated). In this work, we propose an extension of FRACT for multi-shell diffusion MRI (MS-FRACT). We show theoretically and empirically that MS-FRACT yields more accurate ODF estimates than conventional FRACT, while still being predictable with strong theoretical characterization, and without requiring tissue-modeling assumptions.

10. M. C. Chambers, C. Bhushan, J. P. Haldar, R. M. Leahy, D. W. Shattuck.
Correcting Inhomogeneity-Induced Distortion in fMRI using Non-Rigid Registration.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, New York City, 2015, pp. 1364-1367.

Magnetic field inhomogeneities in echo planar images (EPI) can cause large distortion in the phase encoding dimension. In functional MRI (fMRI), this distortion can shift activation loci, increase inter subject variability, and reduce statistical power during group analysis. Distortion correction methods that make use of acquired magnetic field maps have been developed, however, field maps are not always acquired or may not be available to researchers. An alternative approach, which we pursue in this paper, is to estimate the distortion retrospectively by spatially registering the EPI to a structural MRI. We describe a constrained non-linear registration method for correcting fMRI distortion that uses T1-weighted images and does not require field maps. We compared resting state results from uncorrected fMRI, fMRI data corrected with field maps, and fMRI data corrected with our proposed method in data from 20 subjects. The results show that the estimated field maps were similar to the acquired field maps and that the proposed method reduces the overall error in independent component location.

11. J. P. Haldar.
Autocalibrated LORAKS for Fast Constrained MRI Reconstruction.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, New York City, 2015, pp. 910-913.

Low-rank modeling of local k-space neighborhoods (LORAKS) is a recent novel framework for reconstructing MRI images from sparsely-sampled and/or noisy data. Previously-proposed LORAKS-based reconstruction approaches relied on low-rank matrix recovery methods, which were powerful but computationally expensive. In this work, we demonstrate that substantial computational accelerations can be achieved if the nullspaces associated with the low-rank LORAKS matrices are pre-estimated from autocalibration data. In addition to improving computation speed, we also show that autocalibrated LORAKS can have substantial advantages over previous autocalibrated parallel imaging methods.

12. D. Kim, J. P. Haldar.
Nonnegative Matrix Factorization for Tissue Mixture Modeling with Noisy MR Magnitude Image Sequences.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, New York City, 2015, pp. 1028-1031.

Nonnegative matrix factorization (NMF) is a powerful blind source separation method that can be used for nonparametric partial volume mixture modeling in a variety of high-dimensional medical imaging experiments. However, conventional NMF methods can fail to produce meaningful results when the measurements contain substantial non-Gaussian noise. This paper proposes a new NMF modeling approach that is appropriate for noisy MRI magnitude images that follow the noncentral chi (NCC) statistical distribution. We formulate a maximum likelihood optimization problem, which we solve by combining conventional least-squares NMF algorithms with a recent majorize-minimize framework for the NCC distribution. This new approach is applied to real diffusion MRI data, and is demonstrated to yield improved results relative to conventional NMF.

13. T. H. Kim, J. P. Haldar.
SMS-LORAKS: Calibrationless Simultaneous Multislice MRI using Low-Rank Matrix Modeling.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, New York City, 2015, pp. 323-326.

Conventional approaches to accelerated simultaneous multislice (SMS) MRI rely on structured k-space sampling and parallel imaging with known coil sensitivity profiles. In this paper, we introduce a novel framework for SMS MRI that is flexible enough to accommodate a number of different experimental variations: it supports both single-channel and parallel imaging data, both calibration-based and calibrationless k-space sampling trajectories, and Hadamard, Fourier, and random-phase non-Fourier encoding along the slice dimension. Our proposed SMS framework is based on the recently introduced LORAKS framework (low-rank matrix modeling of local k-space neighborhoods). The new framework, which we call SMS-LORAKS, is evaluated using real retrospectively undersampled k-space data. These evaluations confirm the promise and flexibility of the proposed approach.

14. D. Varadarajan, J. P. Haldar.
MS-FRACT: Optimized Linear Transform Methods for ODF Estimation in Multi-Shell Diffusion MRI.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, New York City, 2015, pp. 1172-1175.

This paper proposes a new linear transform approach for multi-shell ODF estimation that has been theoretically characterized and does not require modeling assumptions. The proposed approach, called MS-FRACT, is optimized over the class of all rotationally-invariant linear transforms to yield accurate ODFs. Due to linearity, MS-FRACT yields stable and predictable results, and can be directly interpreted with respect to the true diffusion propagator. The performance of MS-FRACT is illustrated using simulated and real data. In addition to proposing MS-FRACT, a new theoretical framework is also described that can be applied to arbitrary multi-shell linear ODF estimation methods.

#### 2014

1. B. Kim, D. B. Kay, Y. Yi, D. Lee, Y. Chaudhry, J. P. Haldar, R. M. Leahy, C. J. Winstein.
DTI analysis of corticospinal tract using BrainSuite: A potential biomarker of upper extremity therapeutic response to neurorehabilitation in chronic stroke.
Society for Neuroscience 44th Annual Meeting, Washington, DC, 2014. (Abstract)
[toggle abstract]

Corticospinal tract (CST) microstructural characteristics measured by diffusion tensor imaging (DTI) are known to be associated with upper extremity (UE) motor impairment after stroke. However, there is a gap in understanding the relationship between DTI-derived measures and UE motor function changes following neurorehabilitation. This study is part of a larger longitudinal phase-I clinical trial in chronic stroke that aims to determine the optimal dose of therapy for sustained affected arm use after therapy has ended. Our purpose is twofold: First, to establish methods to quantify CST characteristics in lesioned brains using BrainSuite. Second, to determine if UE motor performance changes after treatment in chronic stroke are associated with DTI-based CST measures. Nine chronic stroke participants completed neuroimaging and clinical assessments before and after 12 sessions of a reproducible UE therapy program within 4 months. Imaging data were processed using BrainSuite (version 13a, http://brainsuite.org). Specifically, BrainSuite was used to semi-automatically extract and parcellate the participants' brains from T1-weighted structural MRI images, to correct the diffusion images for geometric distortion, to coregister the diffusion images with the structural images, to compute DTI parameters, to perform deterministic tractography, and to identify the CST based on the set of tracks that pass through both a manually labeled pons region of interest (ROI) and an automatically labeled precentral gyrus ROI. The ipsi- and contra-lesional CST fractional anisotropy (FA) was quantified, and the CST FA asymmetry index [(FAcontra - FAipsi)/(FAcontra + FAipsi)] was calculated. The Wolf motor function test (WMFT) and Fugl-Meyer assessment (FMA) were performed to assess participants' motor function and impairment respectively. Linear regression analysis was performed to examine the relationship between CST FA asymmetry and these clinical outcomes, based on the hypothesis that pre CST FA asymmetry would be correlated with the pre to post changes in the WMFT and FMA scores. Similar to previous reports, the pre CST FA asymmetry was positively correlated with the pre WMFT score. However, the pre and pre to post changes in CST FA asymmetry were not correlated with the pre FMA or pre to post changes in either FMA or WMFT scores. Because of the limited range of pre CST FA asymmetry indices for the nine participants in this study, a relationship between CST FA asymmetry and clinical outcomes could not be explained by our results. Thus, further investigations of DTI-derived measures in post-stroke individuals are necessary to identify biomarkers for functional recovery.

2. M. Chambers, C. Bhushan, T. Pirnia, K. Narr, J. Haldar, R. Leahy, D. Shattuck.
Registration-Based Distortion and Intensity Correction in fMRI.
20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, 2014, p. 3497. (Abstract)

3. J. P. Haldar.
LORAKS: Low-Rank Modeling of Local k-Space Neighborhoods.
Joint Annual Meeting ISMRM-ESMRMB, Milan, 2014, p. 85. (Abstract)
Featured with a PowerPoster presentation (hand-selected as one of the 150 most interesting abstracts out of 6,481 submissions to the conference).

This work presents a novel framework for constrained image reconstruction based on Low-Rank Modeling of Local k-Space Neighborhoods (LORAKS). We first demonstrate that k-space data for low-dimensional images can be mapped into high-dimensional matrices, such that the resulting matrices possess low-rank structure when the original images have limited support and/or slowly-varying phase. Subsequently, we propose a flexible approach to exploiting this low-rank structure that enables image reconstruction from undersampled data. The approach is analogous to a single-channel calibrationless generalization of GRAPPA, and is demonstrated to outperform sparsity-guided reconstructions of undersampled data in certain contexts.

4. D. Varadarajan, J. P. Haldar.
A Novel Approach for Statistical Estimation of HARDI Diffusion Parameters from Rician and Non-Central Chi Magnitude Images.
Joint Annual Meeting ISMRM-ESMRMB, Milan, 2014, p. 801. (Abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.
Featured with a PowerPoster presentation (hand-selected as one of the 150 most interesting abstracts out of 6,481 submissions to the conference).

Noisy MRI magnitude and root sum-of-squares (SoS) images follow the Rician and non-central chi distribution respectively. In diffusion MRI, estimation of diffusion parameters can be inaccurate due to the noise bias introduced by these distributions. This work presents a new approach to model and estimate HARDI parameters from Rician and non-central chi data. We show estimation results from both simulated and noisy real data, and demonstrate how this method can improve estimation compared to existing approaches.

5. J. Zhuo, J. P. Haldar.
P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data.
Joint Annual Meeting ISMRM-ESMRMB, Milan, 2014, p. 745. (Abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

This work presents P-LORAKS, a novel approach to constrained image reconstruction from parallel imaging data. Similar to the original LORAKS (low-rank matrix modeling of local k-space neighborhoods) method, P-LORAKS uses low-rank matrix models to generate parsimonious constrained reconstruction representations of images with limited spatial support and/or slowly varying phase. Combining LORAKS with parallel imaging data leads to further improvements in image reconstruction quality. Results are illustrated with real data, where P-LORAKS compares favorably to existing parallel imaging methods like SPIRiT and SAKE.

6. C. Bhushan, J. P. Haldar, A. A. Joshi, D. Shattuck, R. M. Leahy.
INVERSION: A robust method for co-registration of MPRAGE and Diffusion MRI images.
Joint Annual Meeting ISMRM-ESMRMB, Milan, 2014, p. 2583. (Abstract)

Accurate registration between MPRAGE and diffusion MRI images is essential for many multi-modal neuroimaging studies. We describe a new method, INVERSION (Inverse contrast Normalization for VERy Simple registratION), that robustly aligns MPRAGE and b=0 s/mm2 images by leveraging known "inverted" contrast relationships between these two modalities. We transform the contrast of the b=0s/mm2 image to match the contrast of the MPRAGE image, and achieve consistently accurate registration using the simple sum of squared differences cost function. Unlike most multi-modal registration approaches, INVERSION uses a locally smooth, and frequently convex, cost function that is relatively easy to numerically optimize.

#### 2013

1. S. Ashrafulla, J. P. Haldar, J. C. Mosher, R. M. Leahy.
Causality in variance in electrophysiological data using the ARCH model.
Asilomar Conference on Signals, Systems & Computers, Pacific Grove, 2013, pp. 798-802.

Measurements of electrophysiological activity can be used to infer interactions between different regions of the human brain. In this work, we consider the use of an autoregressive conditional heteroscedasticity (ARCH) model to estimate causality in variance between different brain regions in simulation and continuously measured EEG data. We propose an efficient new algorithm for ARCH model estimation and demonstrate that the proposed approach provides promising results that are distinct from the causality estimates obtained from simpler and more conventional signal causality models.

2. D. Beroukhim, M. Konersman, M. Chong, A. A. Joshi, C. Bhushan, D. W. Shattuck, J. P. Haldar, R. M. Leahy, C. J. Winstein.
Effects of rehabilitation post-stroke: DTI analysis of corticospinal tract characteristics using BrainSuite13.
Society for Neuroscience, San Diego, 2013. (Abstract)
[toggle abstract]

Post stroke upper extremity (UE) motor impairment has been associated with microstructural changes in corticospinal tract (CST) as measured by diffusion tensor imaging (DTI). It is not fully understood how well changes in DTI measures can predict motor recovery and correlate with functional motor changes following neurorehabilitation. This project is part of a larger phase I clinical trial in chronic stroke that aims to determine prospectively the dose of therapy that will lead to continued use of the UE after therapy has ended. Quantification of the CST in a lesioned brain requires a standardized method to identify the CST within and between subjects. Our purpose is twofold. First, to establish a sensitive and specific method to quantify changes in CST characteristics in lesioned brains associated with UE rehabilitation. Second, to investigate the relationship between CST diffusion metrics and initial UE impairment and motor performance changes after rehabilitation. Participants with chronic stroke completed DTI and motor impairment assessments before and after 12 sessions of a reproducible UE therapy program within 4 months. Imaging data were processed using BrainSuite13 (http://brainsuite.loni.ucla.edu) as follows: (i) diffusion images were corrected for susceptibility-induced geometric distortion and co-registered to structural T1-weighted images, (ii) the BrainSuite Atlas was registered to individual subject data to automatically label a set of cortical and subcortical regions of interest (ROIs), (iii) diffusion tensors were computed in the labeled anatomical space, (iv) the major white matter tracts were identified using deterministic tractography. The CST was identified using ROIs for the pons and posterior limb of the internal capsule. We have established a processing pipeline to quantify CST fractional anisotropy (FA) and mean diffusivity (MD). Preliminary results using this method indicate reduced hemispheric asymmetry of FA pre- to post- therapy correlating with improvement in UE motor ability, assessed by the Wolf Motor Function Test time score. Results from 6 patients will be presented to assess the sensitivity, specificity, and clinical usefulness of this approach in the study of focused rehabilitation for chronic stroke. We present a method to reliably identify and quantify changes in CST characteristics, using BrainSuite13 software. This method may prove useful for prospective identification of responders to intensive rehabilitation programs and for revealing mechanisms of neuroplasticity including the attenuation of hemispheric CST asymmetries in chronic stroke.

3. D. Shattuck, A. Joshi, J. Haldar, C. Bhushan, S. Choi, A. Krause, J. Wisnowski, H. Damasio, A. Toga, R. M. Leahy.
New BrainSuite13 Tools for Image Segmentation, Registration, Connectivity Analysis and Visualization.
19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, 2013, p. 1688. (Abstract)

4. S. Choi, C. Bhushan, A. Joshi, K. Raphel, D. Tranel, D. Shattuck, J. Haldar, R. M. Leahy, H. Damasio, J. Wisnowski.
Altered orbitofrontal tissue microstructure in patients with chronic anterior temporal lobe lesions.
19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, 2013, p. 3781. (Abstract)

5. J. P. Haldar, D. W. Shattuck, R. M. Leahy.
Estimation of White Matter Fiber Orientations with the Funk-Radon and Cosine Transform.
International Society for Magnetic Resonance in Medicine 21st Scientific Meeting, Salt Lake City, 2013, p. 771. (Abstract)

Tractography methods depend on estimating orientation distribution functions (ODFs) from diffusion MRI data. This work evaluates the performance of a new ODF estimation method known as the Funk-Radon and Cosine Transform (FRACT). The FRACT is a linear transformation technique for spherically-sampled q-space data that generalizes the previous Funk-Radon Transform (FRT). It estimates the constant solid angle ODF, can be characterized theoretically, can be computed efficiently, and substantially outperforms the FRT. This work compares the FRACT to existing ODF estimation methods with simulated and real data. Results demonstrate that the FRACT can be a powerful tool for MR tractography applications.

6. C. Bhushan, A. A. Joshi, R. M. Leahy, J. P. Haldar.
Accelerating Data Acquisition for Reversed-Gradient Distortion Correction in Diffusion MRI: A Constrained Reconstruction Approach.
International Society for Magnetic Resonance in Medicine 21st Scientific Meeting, Salt Lake City, 2013, p. 55. (Abstract)
Recipient of a Magna Cum Laude ISMRM Merit Award.

EPI-based diffusion MRI suffers from localized distortion artifacts in the presence of B0 inhomogeneity, which can cause problems in multi-modal image analysis and when estimating quantitative diffusion parameters. These distortions can be partially corrected with measured field maps, though performance improves substantially if each image is acquired twice with reversed phase encoding gradients (at the expense of doubling the scan time). In this work, we propose a novel acquisition and reconstruction strategy that leverages a constrained reconstruction formulation to enable accurate distortion correction with similar performance to the reversed gradient method, but without increasing the scan time.

7. D. W. Shattuck, A. A. Joshi, J. P. Haldar, C. Bhushan, S. Choi, A. C. Krause, J. L. Wisnowski, A. W. Toga, R. M. Leahy.
Software Tools for Anatomical ROI-based Connectivity Analysis.
International Society for Magnetic Resonance in Medicine 21st Scientific Meeting, Salt Lake City, 2013, p. 2691. (Abstract)

We describe a collection of software tools for jointly processing and visualizing structural and diffusion MRI of the brain. T1-weighted brain MRI are processed to extract models of the cortical surface. A brain atlas labeled with anatomical ROIs is registered to the subject data using a combined surface/volume registration procedure. Diffusion weighted images are processed to produce fiber tract models. The structural and diffusion results are combined to generate a brain connectivity map based on the set of anatomical ROIs. These tools can be applied using scripts or through a user interface that provides sophisticated interactive processing and visualization capabilities.

8. J. P. Haldar, R. M. Leahy.
The Equivalence of Linear Spherical Deconvolution and Model-Free Linear Transform Methods for Diffusion MRI.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, San Francisco, 2013, pp. 504-507.

This work provides a theoretical analysis of linear spherical deconvolution methods in diffusion MRI, building off of a theoretical framework that was previously developed for model-free linear transforms of the Fourier 2-sphere. It is demonstrated that linear spherical deconvolution methods have an equivalent representation as model-free linear transform methods. This perspective is used to study the characteristics of linear spherical deconvolution from the point of view of the diffusion propagator. Practical results are shown with experimental brain MRI data.

9. D. Varadarajan, J. P. Haldar.
A Quadratic Majorize-Minimize Framework for Statistical Estimation with Noisy Rician- and Noncentral Chi-Distributed MR Images.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, San Francisco, 2013, pp. 708-711.

The statistics of noisy MR magnitude and square-root sum-ofsquares MR images are well-described by the Rice and noncentral chi distributions, respectively. Statistical estimation involving these distributions is complicated by the facts that they have first- and second-order moments that depend nonlinearly on the noiseless image, and can have nonconvex negative log-likelihoods. This paper proposes a new majorize-minimize framework to ease the computational burden associated with statistical estimation involving these distributions. We derive quadratic tangent majorants for the negative loglikelihoods, which enables statistical cost functions to be optimized using a sequence of much simpler least-squares or regularized least-squares surrogate problems. We demonstrate the use of this framework in the context of regularized MR image denoising, with both simulated and experimental data.

10. J. P. Haldar.
Calibrationless Partial Fourier Reconstruction of MR Images with Slowly-Varying Phase: A Rank-Deficient Matrix Recovery Approach.
ISMRM Workshop on Data Sampling & Image Reconstruction, Sedona, 2013. (Abstract)

#### 2012

1. C. Bhushan, J. P. Haldar, A. A. Joshi, R. M. Leahy.
Correcting Susceptibility-Induced Distortion in Diffusion-Weighted MRI using Constrained Nonrigid Registration.
Asia Pacific Signal and Information Processing Association (APSIPA) Annual Summit and Conference, Hollywood, 2012.
Invited Presentation.

Echo Planar Imaging (EPI) is the standard pulse sequence used in fast diffusion-weighted magnetic resonance imaging (MRI), but is sensitive to susceptibility-induced inhomogeneities in the main B0 magnetic field. In diffusion MRI of the human head, this leads to geometric distortion of the brain in reconstructed diffusion images and a resulting lack of correspondence with the high-resolution MRI scans that are used to define the subject anatomy. In this study, we propose and test an approach to estimate and correct this distortion using a non-linear registration framework based on mutual-information. We use an anatomical image as the registration-template and constrain the registration using spatial regularization and physics-based information about the characteristics of the distortion, without requiring any additional data collection. Results are shown for simulated and experimental data. The proposed method aligns diffusion images to the anatomical image with an error of 1-3 mm in most brain regions.

2. J. P. Haldar, Y. Lin, B. Bai, R. M. Leahy.
Edge Artifact Reduction Methods for Iterative PET Reconstruction.
IEEE Medical Imaging Conference, Anaheim, 2012. (Abstract)
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Driven by advances in the modeling of positron emission tomography (PET) data acquisition physics, statistically-based iterative reconstruction methods have lead to significant improvements in the spatial resolution and signal-to-noise ratio of PET images. Despite this progress, iteratively reconstructed images can also demonstrate certain kinds of artifacts that do not typically appear with more classical analytic reconstruction methods. This work considers one such longstanding problem: systematic overshoots and undershoots that manifest near image edges. In this work, we implement and compare several different (existing and new) regularization-based strategies for mitigating edge artifacts in statistical PET reconstruction, including classical linear smoothing methods, edge-preserving nonlinear smoothing methods, dictionary-based reconstructions, and more. Results suggest that some of these methods can be effective at largely eliminating edge artifacts.

3. Y. Lin, J. P. Haldar, Q. Li, R. M. Leahy.
Kinetic Parameter Estimation in Dynamic PET with a Sparsity-Regularized Mixture Model.
IEEE Medical Imaging Conference, Anaheim, 2012. (Abstract)
Recipient of the 1st place MIC student paper award.
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The accuracy of kinetic parameters estimation in dynamic PET is frequently limited by its low signal to noise ratio (SNR). Tissue heterogeneity and partial volume effect further contaminate the estimation results, especially in small tumors. To address these limitations, we propose a sparsity-regularized mixture model in which each image voxel is represented as a mixture of different tissue types with distinct temporal dynamics. A two stage algorithm is proposed to solve the mixture model. In the first stage, a basis based method is applied to estimate the rate parameters for the different tissue compartments incorporating a group sparsity constraint and a tissue sparsity constraint. In the second stage, tissue fraction and linear parameters of tissue time activity curves (TACs) are estimated using a combination of sparsity and spatial-regularity constraints. A block coordinate descent (BCD) algorithm with a manifold search is used to robustly estimate the parameters. The method is evaluated with both simulated and experimental dynamic PET data.

4. S. Ashrafulla, J. P. Haldar, A. A. Joshi, R. M. Leahy.
Canonical Granger Causality.
18th International Conference on Biomagnetism, Paris, 2012. (Abstract)
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Fast recordings, such as those from magnetoencephalography (MEG) or electroencephalography (EEG), can be used to investigate causal functional relationships between different brain regions of interest (ROIs). Previous work has generally measured causality between pairs of time series rather than pairs of anatomical ROIs, each of which may exhibit more complex spatio-temporal behavior requiring two or more time series.
We describe a new scalar metric, canonical Granger Causality (CGC), between two sets of signals that is designed to elicit causality between the two ROIs represented by these sets. Our general approach is to measure Granger causality (GC) from a linear combination of one set of signals to a linear combination of the other. In a manner analogous to the canonical correlation, we define CGC as the maximum of the GC over all linear combinations within each set, as illustrated in the figure below. Thus, we extract from each set of signals the component most strongly influencing the causal network between ROIs. Since our metric is invariant to scaling of the weights, we constrain the 2-norms of the weighting coefficients to be unity, equivalently, for each set the applied weights are constrained to the unit sphere.
We solve for the optimal weights using a gradient descent approach on the product of unit spheres, leveraging computational techniques from optimization on similar submanifolds. To compute GC between linear combinations of signals, we use standard autoregressive modeling and estimation techniques that lead to a closed form expression for the gradient of our cost function. We compare CGC in Monte Carlo simulations to an alternative previously proposed multivariate causality measure, demonstrating that CGC has the potential to more accurately identify causality from short time records. We also demonstrate CGC in applications to MEG and intracranial electroencephalographic (icEEG) recordings from a human subject with epilepsy.

5. J. P. Haldar, D. W. Shattuck, H. Damasio, R. M. Leahy.
Improved Diffusion Tractography with the Funk-Radon and Cosine Transform.
18th Annual Meeting of the Organization for Human Brain Mapping, Beijing, 2012, p. 408. (Abstract)

6. J. Gai, J. L. Holtrop, X.-L. Wu, F. Lam, M. Fu, J. P. Haldar, W.-m. W. Hwu, Z.-P. Liang, B. P. Sutton.
More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPU.
International Society for Magnetic Resonance in Medicine 20th Scientific Meeting, Melbourne, 2012, p. 2550. (Abstract)

We further accelerate the Illinois Massively Parallel Acceleration Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) package to approach clinically-acceptable times while still taking advantage of a variety of advanced image acquisitions and reconstruction techniques. The improved IMPATIENT implemented a faster Toeplitz-based iterative image reconstruction method, whose computation time is further reduced by an optimally tuned, GPU-accelerated gridding implementation. We demonstrate that the Toeplitz code running on a NVIDIA Tesla C1060 (field-corrected, SENSE) can reduce a one-week long, non-Cartesian 3D 1mm3 high-resolution, whole brain DTI reconstruction (4-channel acquisition) to 4.3 hours. These improvements will enable advances in 3D non-Cartesian sequences, such as cones and stacks of spirals.

7. J. P. Haldar, R. M. Leahy.
New Linear Transforms for Data on a Fourier 2-Sphere with Application to Diffusion MRI.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Barcelona, 2012, pp. 402-405.

This paper describes a new family of linear transforms for data restricted to the surface of a 2-sphere in three-dimensional Fourier space. These transforms generalize the existing Funk-Radon Transform, which has previously been used with great success to extract microstructural tissue orientation information from high angular resolution magnetic resonance diffusion imaging data. Several properties of the new transforms are described, and computationally efficient implementations are derived using spherical harmonic basis functions. A special case from this family, called the Funk-Radon and Cosine Transform, is introduced and evaluated. The method is illustrated with simulated and real diffusion weighted MRI data.

8. S. Ashrafulla, J. P. Haldar, A. A. Joshi, R. M. Leahy.
Canonical Granger Causality Applied to Functional Brain Data.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Barcelona, 2012, pp. 1751-1754.

Dynamic images of functional activity in the brain offer the potential to measure connectivity between regions of interest. We want to measure causal activity between regions of interest (ROIs) with signals recorded from multiple channels or voxels in each ROI. Previous methods, such as Granger causality, look for causality between individual time series; hence, they suffer from local interactions or interferers obscuring signals of interest between two ROIs. We propose a metric that reduces the effect of interference by taking weighted sums of sensors in each ROI, as is done with canonical correlation. Hence, we measure region-to-region, rather than channel-to-channel or point-to-point, Granger causality. We show in simulation that our "canonical Granger causality" accurately mimics the underlying structure with few samples, unlike current methods of multivariate Granger causality. We then use anatomically relevant regions of interest in a visuomotor task in a multichannel intracortical EEG study to infer the direction of transmission in visual processing.

9. F. Lam, S. D. Babacan, J. P. Haldar, N. Schuff, Z.-P. Liang.
Denoising Diffusion-Weighted MR Image Sequences using Low Rank and Edge Constraints.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Barcelona, 2012, pp. 1401-1404.

This paper addresses the denoising problem associated with diffusion MR imaging. Building on previous approaches to this problem, this paper presents a new method for joint denoising of a sequence of diffusion-weighted (DW) magnitude images. The proposed method uses a maximum a posteriori (MAP) estimation formulation to incorporate a Rician likelihood (for modeling the noisy magnitude data), a low rank model (for the DW image sequences) and a spatial prior (for imposing joint edge constraints). An efficient algorithm to solve the associated optimization problem is also described. The proposed method has been evaluated using both simulated and experimental diffusion tensor imaging (DTI) data, which yields very encouraging results both qualitatively and quantitatively.

10. Y. Lin, Q. Li, J. P. Haldar, R. M. Leahy.
Constrained Mixture Modeling for the Estimation of Kinetic Parameters in Dynamic PET.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Barcelona, 2012, pp. 1004-1007.

The estimation and analysis of kinetic parameters in dynamic PET is frequently confounded by noise and partial volume effects. We propose a new constrained model of dynamic PET to address these limitations. The proposed formulation incorporates an explicit partial volume model in which each image voxel is represented as a mixture of different pure tissue types with distinct temporal dynamics. A two stage algorithm is proposed to solve the resulting problem. In the first stage, a sparse signal processing method is applied to estimate the rate parameters for the different tissue compartments from the noisy PET time series. In the second stage, tissue fractions and the linear parameters of different time activity curves (TACs) are estimated using a combination of sparsity, spatial-regularity, and fractional mixture constraints. A block coordinate descent (BCD) algorithm is combined with a manifold search to robustly estimate these parameters. The method is evaluated with both simulated and experimental dynamic PET data.

11. D. Clewett, J. Haldar, H. Damasio, M. Mather.
Subregions of the thalamus connected with temporal and parietal cortex show greater age-related variation than other subregions.
Cognitive Neuroscience Society, Chicago, 2012. (Abstract)
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As a central relay station to cortex, the thalamus plays a critical role in the facilitation of sensory, motor, memory and executive processes. Distinct patterns of thalamo-cortical connectivity reflect the functionality of separate thalamic nuclei and relates to normal brain function. While previous studies have focused on disorders associated with thalamic pathology, little is known about how normal aging may affect specific sub-regions of the thalamus and their connections to cortical brain regions. To address this issue, we used diffusion tensor imaging (DTI) to examine thalamocortical connectivity in vivo in three age groups ranging from younger adults to older adults. Probabilistic tractography was used to trace connectivity between the left and right thalami and six cortical target regions. Putative nuclei were delineated for individual subjects via connectivity-based segmentation of the thalamus, such that subdivisions were determined by the cortical target with the highest probability of connectivity. Fractional Anisotropy (FA) and Mean Diffusivity (MD) values were extracted from the derived nuclei to localize and quantify age-related changes in microstructural integrity. Global decline in thalamic size and cortical connectivity was observed in older adults. Statistically significant degeneration with age was found in sub-regions predominantly connected to the frontal and temporal lobes, while sensory and motor regions were relatively spared. Changes in the spatial distribution of thalamo-temporal connections also suggests age-related decline in the mediodorsal nucleus of the thalamus, an area implicated in emotion and working memory. We conclude that differential thalamic degeneration may contribute to cognitive decline associated with normal aging.

#### 2011

1. S.-L. Liew, K. A. Garrison, J. Haldar, C. J. Winstein, H. Damasio, L. Aziz-Zadeh.
Structural neuroanatomy of lesioned brains in individuals with chronic stroke and functional correlations with action observation networks.
Society for Neuroscience, Washington, D.C., 2011. (Abstract)
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Stroke is the leading cause of disability in adults, often resulting in lasting motor impairments that hinder one's ability to engage in daily activities. Recent rehabilitation research has focused on ways to activate damaged motor regions through action observation, by engaging the putative human mirror neuron system (MNS). The MNS is a neural network comprised of premotor and parietal motor-related regions that are active both during the execution of an action and the observation of the same or similar actions. Thus, observing actions may lead to increased motor cortical activity in the lesioned cortex, even in the absence of overt movement. Recent evidence suggests that therapy involving action observation in conjunction with physical practice provides functional gains (Ertelt et al., 2007; Franchescini et al., 2010). However, it is unclear how individual differences in the underlying structural anatomy of the post-stroke brain may influence activity in these motor-related brain regions. Such information can provide novel insight into understanding the basic mechanisms behind structure-function relationships in motor-related networks after stroke.
Our current analysis utilized high-resolution structural MRIs in 12 participants with chronic stroke resulting in moderate-to-severe right dominant upper limb hemiparesis, and 12 age-matched non-disabled participants with no known neurological deficits. Participants then observed grasp actions during functional MRI. Anatomical images were analyzed in BrainVox, including manual brain extractions and hand-drawn lesion and region of interest tracings. We then correlated the BOLD response in MNS and motor cortical regions with the following factors: total lesion volume, percent of lesion overlap in regions of interest, grey and white matter volume, and amount of cortical atrophy, as well as behavioral motor scores from the Wolf Motor Function Test and the Upper Extremity Fugl-Meyer Assessment. Results indicate that structural measures related to stroke correlate with region of interest parameter estimates in the MNS in participants with chronic stroke. In addition, functional activation of the MNS correlated with behavioral measures of motor performance. Our findings suggest that the structural anatomy of the lesioned brain may provide useful information about which patients may benefit from methods that engage the MNS for stroke rehabilitation by highlighting the interplay between structural neuroanatomy, functional activation of motor-related circuits, and motor ability.

2. J. P. Haldar, J. H. Kim, S.-K. Song, Z.-P. Liang.
Accelerated Mouse Spinal Cord Diffusion Measurements with SNR-Enhancing Joint Reconstruction.
International Society for Magnetic Resonance in Medicine 19th Scientific Meeting, Montreal, 2011, p. 2073. (Abstract)

Diffusion imaging experiments have previously been demonstrated to accurately quantify spinal cord white matter injury and disease in various rodent models. One limitation of these experiments is that substantial signal averaging has been necessary to achieve sufficient signal-to-noise ratio (SNR). Averaging necessitates long imaging experiments, which can be stressful for imaging subjects and limits throughput. In this work, we demonstrate that an appropriate statistical denoising strategy can be used in place of averaging, leading to experiments that are 4X faster but are still capable of quantifying spinal cord disease and injury in mouse models of multiple sclerosis and trauma.

3. A. G. Christodoulou, C. Brinegar, B. Zhao, J. P. Haldar, H. Zhang, Y.-J. L. Wu, T. K. Hitchens, C. Ho, Z.-P. Liang.
First-Pass Myocardial Perfusion Imaging with Sparse (k,t)-Space Sampling.
International Society for Magnetic Resonance in Medicine 19th Scientific Meeting, Montreal, 2011, p. 2045. (Abstract)

Myocardial perfusion imaging is an important and challenging application of cardiovascular MRI. This work demonstrates that sparse sampling of (k,t)-space with the joint use of partial and spatial-spectral sparsity constraints can significantly improve the spatiotemporal resolution of first-pass myocardial perfusion imaging experiments. Experimental results in rats show a 390 μm in-plane spatial resolution and 15 ms temporal resolution, representing an equivalent acceleration factor of 51.

4. B. Zhao, J. Haldar, A. Christodoulou, Z.-P. Liang.
Image Reconstruction from Highly Undersampled (k, t)-space Data with Joint Partial Separability and Sparsity Constraints.
International Society for Magnetic Resonance in Medicine 19th Scientific Meeting, Montreal, 2011, p. 4375. (Abstract)

Sparse sampling is emerging as an effective tool to further accelerate MRI. Previous work has shown that partial separability and sparsity constraints are each able to individually reduce sampling requirement below the Nyquist rate. In this abstract, we present a new reconstruction method that enables using partial separability and sparsity constraints jointly. The joint use of these constraints enables high resolution reconstruction from sparsely sampled data.

5. X.-L. Wu, J. Gai, F. Lam, M. Fu, J. P. Haldar, Y. Zhuo, Z.-P. Liang, W.-M. Hwu, B. P. Sutton.
IMPATIENT MRI: Illinois Massively Parallel Acceleration Toolkit for Image reconstruction with ENhanced Throughput in MRI.
International Society for Magnetic Resonance in Medicine 19th Scientific Meeting, Montreal, 2011, p. 4396. (Abstract)

Despite advances in acquisition and reconstruction technologies, typical clinical scans rely on Cartesian acquisitions and limited reconstruction routines. Requirements for significant computational resources and specialized expertise are a barrier to widespread use of algorithms that combine efficient non-Cartesian trajectories, field inhomogeneity correction, parallel imaging, and image regularization. We present a parallel implementation of such a reconstruction utilizing manycore graphics processing cards to speed reconstruction to acceptable levels, even for large matrix sizes and multiple coil acquisitions. We compare reconstruction times with parallel C-code and a common approximation method, showing that the proposed code is faster without using interpolation operators.

6. J. P. Haldar, Z.-P. Liang.
Low-Rank Approximations for Dynamic Imaging.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Chicago, 2011, pp. 1052-1055.
Invited Presentation.

This paper describes a framework for dynamic imaging based on the representation of a spatiotemporal image as a low-rank matrix. This kind of image modeling is flexible enough to accurately and parsimoniously represent a wide range of dynamic imaging data. Representation using a low-rank model leads to new schemes for data acquisition and image reconstruction, enabling reconstruction from highly-undersampled datasets. Theoretical considerations and algorithms are discussed, and empirical results are provided to illustrate the performance of the approach.

7. J. P. Haldar, Z.-P. Liang.
On MR Experiment Design with Quadratic Regularization.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Chicago, 2011, pp. 1676-1679.

The design of MRI experiments represents a trade-off between acquisition time, signal-to-noise ratio (SNR), and resolution. For fixed acquisition time and reconstruction resolution, it has been widely believed that the optimal acquisition strategy is to avoid collecting k-space data at frequencies higher than the nominal image resolution. While this belief is true under certain metrics, we observe in this work that a high-resolution acquisition strategy, combined with an appropriate linear filtering/regularization strategy, leads to significantly improved SNR/resolution efficiency for the majority of common resolution metrics. Analysis of this surprising result leads to practical methods for the improved design of imaging experiments and the selection of efficient quadratic regularization penalties.

8. X.-L. Wu, J. Gai, F. Lam, M. Fu, J. P. Haldar, Y. Zhuo, Z.-P. Liang, W.-m. Hwu, B. P. Sutton.
IMPATIENT MRI: Illinois Massively Parallel Acceleration Toolkit for Image reconstruction with ENhanced Throughput in MRI.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Chicago, 2011, pp. 69-72.

Much progress has been made in the design of efficient acquisition trajectories for high spatial and temporal resolution in magnetic resonance imaging (MRI). Additionally, significant developments in image reconstruction have enabled the reconstruction of reasonable images from massively undersampled or noisy data that is corrupted by a variety of physical effects, including magnetic field inhomogeneity. Translation of these techniques into clinical imaging has been impeded by the need for expertise and computational facilities to realize the potential of these methods. We present the Illinois Massively Parallel Acceleration Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI), a reconstruction utility that enables advanced techniques within clinically relevant computation times by using the computational power available in low-cost graphics processing cards.

9. F. Lam, J. P. Haldar, Z.-P. Liang.
Motion Compensation for Reference-Constrained Image Reconstruction from Limited Data.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Chicago, 2011, pp. 73-76.

Using a reference image (or a template) to constrain image reconstruction from limited data is becoming more and more popular in various imaging applications. However, in order for a reference/template to be a useful constraint, it has to be correctly aligned with the target image to be determined. This paper addresses this new image registration problem of registering a high-resolution image to a target image of which only limited measurements are available. We solve this problem using an intermediate image model, which expresses the target image as a combination of a generalized series (with basis constructed from a motion-dependent reference image) and a residual component. An algorithm is proposed to determine the motion parameters. Performance of the proposed method has been analyzed by computer simulations. Accurate motion compensation is demonstrated. The proposed method is expected to make image reconstruction using prior information from a reference more robust in the presence of object motion.

10. B. Zhao, J. P. Haldar, A. G. Christodoulou, Z.-P. Liang.
Further development of image reconstruction from highly undersampled (k, t)-space data with joint partial separability and sparsity constraints.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Chicago, 2011, pp. 1593-1596.

Joint use of partial separability (PS) and spatial-spectral sparsity constraints has previously been demonstrated useful for image reconstruction from undersampled data. This paper extends our early work in this area by proposing a new method for jointly enforcing the PS and spatial total variation (TV) constraints for dynamic MR image reconstruction. An algorithm is also described to solve the underlying optimization problem efficiently. The proposed method has been validated using simulated cardiac imaging data, with the expected capability to reduce image artifacts and reconstruction noise.

11. X.-L. Wu, Y. Zhuo, J. Gai, F. Lam, M. Fu, J. P. Haldar, W.-m. Hwu, Z.-P. Liang, B. P. Sutton.
Advanced MRI reconstruction toolbox with accelerating on GPU.
Proceedings of SPIE, vol. 7872, 2011, p. 78720Q.

In this paper, we present a fast iterative MR image reconstruction algorithm taking advantage of the prevailing GPGPU programming paradigm. In clinical environment, MR image reconstruction is usually performed via fast Fourier transform (FFT). However, imaging artifacts (signal loss and signal distortions) resulting from susceptibility-induced magnetic field inhomogeneities degrade the quality of reconstructed images. These artifacts must be addressed using accurate modeling of the physics of the system coupled with iterative reconstruction. We have developed a reconstruction algorithm with improved image quality at the expense of computation time. Hence, an implementation on GPUs is proposed, achieving significant speedup. The proposed algorithm implements a conjugate gradient reconstruction using explicit Fourier transform (FT) in order to model the field inhomogeneity and its gradients. In addition, a smoothing constraint is included in the form of sparse matrix regularization in order to reduce noise in reconstructed images. We apply the compilation optimizations from levels of algorithm, program code structures, and specific architecture performance tuning, featuring both our MRI reconstruction algorithm and GPU hardware specifics. The current GPU implementation produces accurate image estimates while accelerating the reconstruction by two orders of magnitudes. Future directions include further optimization of current and higher-dimension approach.

#### 2010

1. Y. Zhuo, B. Sutton, X.-L. Wu, J. Haldar, W.-m. Hwu, Z.-P. Liang.
Sparse Regularization in MRI Iterative Reconstruction Using GPUs.
3rd International Conference on Biomedical Engineering and Informatics, Yantai, 2010, pp. 578-582.

Regularization is a common technique used to improve image quality in inverse problems such as MR image reconstruction. In this work, we extend our previous Graphics Processing Unit (GPU) implementation of MR image reconstruction with compensation for susceptibility-induced field inhomogeneity effects by incorporating an additional quadratic regularization term. Regularization techniques commonly impose the prior information that MR images are relatively smooth by penalizing large changes in intensity between neighboring voxels. However, the associated computations often increase data access and the overall computational load, which can lead to slower image reconstruction. This motivates us to adopt a GPU-enabled implementation of spatial regularization using sparse matrices. This implementation enables the computations for the entire reconstruction procedure to be done on the GPU, which avoids the memory bandwidth bottlenecks associated with frequent communications between the GPU and CPU. Both the CPU and GPU code of this implementation will be available for release at the time of the conference.

2. J. P. Haldar, Z. Wang, G. Popescu, Z.-P. Liang.
Label-Free High-Resolution Imaging of Live Cells With Deconvolved Spatial Light Interference Microscopy.
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, 2010, pp. 3382-3385.
PubMed Central ID: PMC3108816.
Recipient of the 1st place award in the EMBC 2010 Student Paper Competition.

Spatial light interference microscopy (SLIM) is a powerful new quantitative phase optical imaging technique that can be used for studying live cells without the need for exogenous contrast agents. This paper proposes a novel deconvolution-based approach to reconstructing SLIM data, which dramatically improves the visual quality of the images. The proposed deconvolution formulation is tailored to the physics of SLIM imaging of biological samples, and a new fast algorithm is designed for computationally-efficient image reconstruction in this setting. Simulation and experimental results demonstrate that deconvolution can reduce the width of the point-spread function by at least 20%, and can significantly improve the contrast of high-resolution features. Temporally-resolved SLIM imaging with the high spatial resolution enabled by deconvolution provides new opportunities for studying the dynamics of cellular and sub-cellular processes.

3. A. G. Christodoulou, C. Brinegar, J. P. Haldar, H. Zhang, Y.-J. L. Wu, L. M. Foley, T. K. Hitchens, Q. Ye, C. Ho, Z.-P. Liang.
High-Resolution Cardiac MRI Using Partially Separable Functions and Weighted Spatial Smoothness Regularization.
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, 2010, pp. 871-874.
PubMed Central ID: PMC3115597.

Imaging of cardiac morphology and functions in high spatiotemporal resolution using MRI is a challenging problem due to limited imaging speed and the inherent tradeoff between spatial resolution, temporal resolution, and signal-to-noise ratio (SNR). The partially separable function (PSF) model has been shown to achieve high spatiotemporal resolution but can lead to noisy reconstructions. This paper proposes a method to improve the SNR and reduce artifacts in PSF-based reconstructions through the use of anatomical constraints. These anatomical constraints are obtained from a high-SNR image of composite (k,t)-space data (summed along the time axis) and used to regularize the PSF reconstruction. The method has been evaluated on experimental data of rat hearts to achieve 390 μm in-plane resolution and 15 ms temporal resolution.

4. X. Peng, H. Nguyen, J. Haldar, D. Hernando, X.-P. Wang, Z.-P. Liang.
Correction of Field Inhomogeneity Effects on Limited k-Space MRSI Data using Anatomical Constraints.
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, 2010, pp. 883-886.

Magnetic field inhomogeneity is a long-standing problem in magnetic resonance imaging (MRI), and spectroscopic imaging (MRSI). Specifically, in MRSI, field inhomogeneity, if not corrected, can cause frequency shifts, line broadening, and lineshape distortions in the spectral peaks. This paper addresses the problem of correcting the field inhomogeneity effects on limited k-space MRSI data. A penalized maximum-likelihood method is proposed, which enables the use of anatomical constraints for improving the correction performance with only limited k-space data. Simulation results are shown to demonstrate the effectiveness of the proposed method.

5. B. Zhao, J. P. Haldar, Z.-P. Liang.
PSF Model-Based Reconstruction with Sparsity Constraint: Algorithm and Application to Real-Time Cardiac MRI.
32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Buenos Aires, 2010, pp. 3390-3393.
PubMed Central ID: PMC3121182.

The partially separable function (PSF) model has been successfully used to reconstruct cardiac MR images with high spatiotemporal resolution from sparsely sampled (k,t)-space data. However, the underlying model fitting problem is often ill-conditioned due to temporal undersampling, and image artifacts can result if reconstruction is based solely on the data consistency constraints. This paper proposes a new method to regularize the inverse problem using sparsity constraints. The method enables both partial separability (or low-rank) and sparsity constraints to be used simultaneously for high-quality image reconstruction from undersampled data. The proposed method is described and reconstruction results with cardiac imaging data are presented to illustrate performance.

6. L.-W. Kuo, J. P. Haldar, Y.-C. Lo, C.-L. Liu, Z.-P. Liang, W.-Y. I. Tseng.
Quantitative Improvement of Diffusion Spectrum Imaging Tractography using Statistical Denoising.
ISMRM-ESMRMB Joint Annual Meeting, Stockholm, 2010, p. 1669. (Abstract)

Noise contamination is a significant problem in diffusion spectrum imaging (DSI) tractography, and previous work has proposed a statistical denoising algorithm to mitigate the effects of low signal-to-noise ratio. In this work, improvements to fiber orientation accuracy due to denoising were quantified using a systematic analysis of angular precision and dispersion metrics. Results show that the proposed denoising method significantly improves angular precision and dispersion. Furthermore, the tractography results demonstrate better reconstruction of white-matter structures using the denoised data. Future work will use the proposed denoising algorithm to improve spatial resolution and reduce scan time.

7. Y. Zhuo, X.-L. Wu, J. P. Haldar, W.-m. W. Hwu, Z.-P. Liang, B. P. Sutton.
Multi-GPU Implementation for Iterative MR Image Reconstruction with Field Correction.
ISMRM-ESMRMB Joint Annual Meeting, Stockholm, 2010, p. 2942. (Abstract)

Nowadays Graphics Processing Units (GPU) leads high computation performance in science and engineering application. We propose a multi-GPU implementation for iterative MR image reconstruction with magnetic field inhomogeneity compensation. The imaging model includes the physics of field inhomogeneity map and its gradients, and thus can compensate for both geometric distortion and signal loss. The iterative reconstruction algorithm is realized on C-language based on Compute Unified Device Architecture (CUDA). Result shows the performance of multi-GPU gains significant speedup by two orders of magnitude. Therefore, the fast implementation make the clinical and cognitive science requirements are achievable for accurate MRI reconstruction.

8. J. P. Haldar, Z.-P. Liang.
Spatiotemporal Imaging With Partially Separable Functions: A Matrix Recovery Approach.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Rotterdam, 2010, pp. 716-719.
Recipient of an IEEE ISBI 2010 Best Student Paper Award.

There has been significant recent interest in fast imaging with sparse sampling. Conventional imaging methods are based on Shannon-Nyquist sampling theory. As such, the number of required samples often increases exponentially with the dimensionality of the image, which limits achievable resolution in high-dimensional scenarios. The partially-separable function (PSF) model has previously been proposed to enable sparse data sampling in this context. Existing methods to leverage PSF structure utilize tailored data sampling strategies, which enable a specialized two-step reconstruction procedure. This work formulates the PSF reconstruction problem using the matrix-recovery framework. The explicit matrix formulation provides new opportunities for data acquisition and image reconstruction with rank constraints. Theoretical results from the emerging field of low-rank matrix recovery (which generalizes theory from sparse-vector recovery) and our empirical results illustrate the potential of this new approach.

9. B. Zhao, J. P. Haldar, C. Brinegar, Z.-P. Liang.
Low Rank Matrix Recovery for Real-Time Cardiac MRI.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Rotterdam, 2010, pp. 996-999.

Real-time cardiac MRI is a very challenging problem because of limitations on imaging speed and resolution. To address this problem, the (k,t)-space MR signal is modeled as being partially separable along the spatial and temporal dimensions, which results in a rank-deficient data matrix. Image reconstruction is then formulated as a low-rank matrix recovery problem, which is solved using emerging low-rank matrix recovery techniques. In this paper, the PowerFactorization algorithm is applied to efficiently recover the cardiac data matrix. Promising results are presented to demonstrate the performance of this novel approach.

10. H. M. Nguyen, J. P. Haldar, M. N. Do, Z.-P. Liang.
Denoising of MR Spectroscopic Imaging Data with Spatial-Spectral Regularization.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Rotterdam, 2010, pp. 720-723.

Low signal-to-noise ratio has been a significant limitation for clinical applications of magnetic resonance spectroscopic imaging (MRSI). This paper investigates a new scheme for denoising MRSI data, incorporating both an anatomically-adapted spatial-smoothness constraint and an autoregressive spectral constraint within the penalized maximum-likelihood framework. Both theoretical analysis and simulation results are provided to characterize the denoising performance of this approach.

11. Y. Zhuo, X.-L. Wu, J. P. Haldar, W.-m. Hwu, Z.-P. Liang, B. P. Sutton.
Accelerating Iterative Field-Compensated MR Image Reconstruction on GPUs.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Rotterdam, 2010, pp. 820-823.

We propose a fast implementation for iterative MR image reconstruction using Graphics Processing Units (GPU). In MRI, iterative reconstruction with conjugate gradient algorithms allows for accurate modeling the physics of the imaging system. Specifically, methods have been reported to compensate for the magnetic field inhomogeneity induced by the susceptibility differences near the air/tissue interface in human brain (such as orbitofrontal cortex). Our group has previously presented an algorithm for field inhomogeneity compensation using magnetic field map and its gradients. However, classical iterative reconstruction algorithms are computationally costly, and thus significantly increase the computation time. To remedy this problem, one can utilize the fact that these iterative MR image reconstruction algorithms are highly parallelizable. Therefore, parallel computational hardware, such as GPU, can dramatically improve their performance. In this work, we present an implementation of our field inhomogeneity compensation technique using NVIDA CUDA(Compute Unified Device Architecture)-enabled GPU. We show that the proposed implementation significantly reduces the computation times by two orders of magnitude (compared with non-GPU implementation) while accurately compensating for field inhomogeneity.

#### 2009

1. H. M. Nguyen, Z. J. Gahvari, J. P. Haldar, M. N. Do, Z.-P. Liang.
Cramér-Rao Bound Analysis of Echo Time Selection for 1H-MR Spectroscopy.
31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Minneapolis, 2009, pp. 2692-2695.

The choice of echo time (TE) is a complicated and controversial issue in proton MR spectroscopy, and represents a balancing act between signal-to-noise ratio and signal complexity. The TE values used in previous literature were selected either heuristically or based on limited empirical studies. In this work, we reconsider this problem from an estimation theoretic perspective. Specifically, we analyze the Cramér-Rao lower bound on estimated spectral parameters as a function of TE, which serves as a metric to quantify the reliability of the estimation procedure. This analysis reveals that a good choice of TE often depends on the particular metabolite of interest, and is a function of both the coupling properties of the metabolites and the general complexity of the spectrum.

2. J. P. Haldar, D. Hernando, Z.-P. Liang.
Super-Resolution Reconstruction of MR Image Sequences with Contrast Modeling.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Boston, 2009, pp. 266-269.

Quantitative MR imaging experiments (e.g., to measure relaxation and diffusion properties of tissues) often require image sequences with different contrast in each frame. However, high-resolution acquisition of each frame can lead to prohibitively long experiments. In this work, we investigate the possibility of utilizing a parametric contrast model to synthesize high-resolution information. Theoretical analysis and empirical evidence indicates that this kind of super-resolution can be possible, though robustness is dependent on a number of factors (e.g., the contrast model and the experiment design). In particular, it is found that conventional low-frequency sampling leads to significant information loss, but that alternative experiments can overcome this limitation. Experimental results are shown in the context of T2* relaxation mapping.

3. W.-m. W. Hwu, D. Nandakumar, J. Haldar, I. C. Atkinson, B. Sutton, Z.-P. Liang, K. R. Thulborn.
Accelerating MR Image Reconstruction on GPUs.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Boston, 2009, pp. 1283-1286.

With the explosive development of advanced image reconstruction algorithms, there is an urgent need for acceleration of these algorithms to facilitate their use in practical applications. This paper describes our experience using graphics processing units (GPUs) for advanced MR image reconstruction from non-Cartesian data. We show that implementation of MR image reconstruction on NVIDIA CUDA-enabled GPUs can significantly accelerate the solution of this type of image reconstruction problem. Given the acceleration afforded by the GPU, we expect our strategy to be applied to other computationally intensive imaging algorithms.

4. J. P. Haldar, K. Sakaie, Z.-P. Liang.
Resolution and Noise Properties of Linear Phase-Constrained Partial Fourier Reconstruction.
International Society for Magnetic Resonance in Medicine 17th Scientific Meeting, Honolulu, 2009, p. 2862. (Abstract)

Phase-constrained partial Fourier (PF) reconstruction is a classical technique that leverages prior knowledge of the image phase to reduce k-space sampling requirements. While the technique has seen wide use, the characteristics of PF reconstructions are usually only evaluated empirically. In this work, we show that resolution and noise properties of the class of linear PF reconstruction methods (including homodyne, projection onto convex sets with linear projections, and matrix inversion methods) can be characterized theoretically in terms of spatial response functions and interference response functions. We demonstrate an application of these theoretical characterizations in the context of regularized PF reconstruction.

5. J. P. Haldar, Q. Gao, X. J. Zhou, Z.-P. Liang.
Optimized Measurement of Anomalous Diffusion.
International Society for Magnetic Resonance in Medicine 17th Scientific Meeting, Honolulu, 2009, p. 3570. (Abstract)

The stretched exponential curve has recently been proposed to model the non-exponential diffusion-induced signal attenuation observed in biological tissues at large b-values. In this work, we propose two techniques to help improve the robustness of the experiment to measure the parameters of this model. First, using the Cramér-Rao bound, we optimize the set of b-values acquired during the experiment. Second, we make use of a regularized joint image reconstruction technique to help mitigate the effects of measurement noise. The combination of these two techniques enables efficient and robust characterization of anomalous diffusion.

6. D. Hernando, P. Kellman, J. Haldar, Z.-P. Liang.
Robust Water/Fat Separation in the Presence of Large Field Inhomogeneities Using a Graph Cut Algorithm.
International Society for Magnetic Resonance in Medicine 17th Scientific Meeting, Honolulu, 2009, p. 459. (Abstract)
Recipient of the ISMRM 2009 I. I. Rabi Young Investigator Award.

Water/fat separation is a classical problem for in vivo MRI. Although many methods have been proposed, robust water/fat separation is still challenging, especially in the presence of large field inhomogeneities. This work tackles the problem using a statistically-motivated formulation which jointly estimates the complete field map and water/fat images. This formulation results in a difficult (high-dimensional and non-convex) minimization problem, which is solved using a novel graph cut algorithm. The proposed method has good theoretical properties and an efficient implementation. It has proven effective for characterizing intramyocardial fat, producing robust water/fat separation in cases containing large field inhomogeneities due to susceptibility effects and magnet imperfections.

7. D. Hernando, D. C. Karampinos, K. F. King, J. Haldar, J. G. Georgiadis, Z.-P. Liang.
Removal of Olefinic Fat Signal in Body Diffusion-Weighted EPI Using a Dixon Method.
International Society for Magnetic Resonance in Medicine 17th Scientific Meeting, Honolulu, 2009, p. 2064. (Abstract)

The signal from olefinic fat protons in body DW-EPI is typically unaffected by chemical shift-based fat suppression methods, and introduces severe bias in the estimation of diffusion parameters. In this work, we propose a Dixon method for robust separation of water and olefinic fat signal. The proposed method uses magnitude images to avoid the phase distortions typical of DW-EPI. The method is demonstrated on phantom and in vivo datasets, and its performance is evaluated using Cramer-Rao bound analysis.

8. Q. Gao, J. P. Haldar, N. Rangwala, R. L. Magin, Z.-P. Liang, X. J. Zhou.
Analysis of High b-Value Diffusion Images Using a Fractional Order Diffusion Model with Denoising Image Reconstruction.
International Society for Magnetic Resonance in Medicine 17th Scientific Meeting, Honolulu, 2009, p. 1418. (Abstract)

Low signal-to-noise ratio (SNR) has been a major source of error in quantitative analyses of diffusion images with high b-values. In this study, we have applied a statistical model for joint reconstruction and denoising on a set of images acquired from the human brain with b-values up to 3,300 s/mm2. The denoised images were analyzed using a fractional order (FO) diffusion model to obtain a set of diffusion parameters. With a more than two-fold increase in SNR and a negligible compromise of spatial resolution, the accuracy of the diffusion parameters has been considerably improved, making it possible to apply complex diffusion analysis with high b-values to patient studies.

#### 2008

1. J. P. Haldar, T.-H. Wu, Q. Wang, C.-I. Chen, S.-K. Song, Z.-P. Liang.
Further Development in Anatomically Constrained MR Image Reconstruction: Application to Multimodal Imaging of Mouse Stroke.
30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, 2008, pp. 422-425.

MR imaging can leverage a wide variety of intrinsic contrast mechanisms to provide detailed information regarding the anatomy, function, physiology, and metabolism of biological tissues. However, because of low sensitivity, many experiments that reveal higher-order structure and function have been limited due to inherent trade-offs between data acquisition time, signal-to-noise ratio, and resolution. This paper describes the further development of a statistical framework for MR image reconstruction which helps to mitigate these effects. Specifically, we advocate the collection of high-resolution multi-modal MR imaging data, and utilize the correlation between features in these different images to reduce noise while maintaining resolution. The proposed approach is illustrated with joint reconstruction of relaxometry and spectroscopic imaging data in a mouse model of stroke.

2. D. Hernando, P. Kellman, J. P. Haldar, Z.-P. Liang.
A Network Flow Method for Improved MR Field Map Estimation in the Presence of Water and Fat.
30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, 2008, pp. 82-85.
EMBS Student Paper Competition Geographic Finalist: North America.

Field map estimation is an important problem in MRI, with applications such as water/fat separation and correction of fast acquisitions. However, it constitutes a nonlinear and severely ill-posed problem requiring regularization. In this paper, we introduce an improved method for regularized field map estimation, based on a statistically motivated formulation, as well as a novel algorithm for the solution of the corresponding optimization problem using a network flow approach. The proposed method provides theoretical guarantees (local optimality with respect to a large move), as well as an efficient implementation. It has been applied to the water/fat separation problem and tested on a number of challenging datasets, showing high-quality results.

3. I. C. Atkinson, A. Lu, J. P. Haldar, Z.-P. Liang, K. R. Thulborn.
Human 17-Oxygen Imaging at 9.4T and Enhanced Reconstruction using 23-Sodium.
American Society of Neuroradiology 46th Annual Meeting, New Orleans, 2008, p. 214. (Abstract)

4. J. P. Haldar, Z.-P. Liang.
Joint Reconstruction of Noisy High-Resolution MR Image Sequences.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Paris, 2008, pp. 752-755.

Quantitative MR studies often utilize sequences of coregistered images, where the contrast in each image frame is experimentally manipulated to enable the regression of important physical parameters. However, the potential of these experiments has been limited for high-resolution biological studies because of long acquisition times and limited signal-to-noise ratio. This work presents a new approach for the reconstruction of an image sequence from noisy data, using a statistical model that incorporates an implicit line-site prior to take advantage of the high level of inter-frame correlation between spatial image features. Reconstructions are efficiently computed using a globally-convergent half-quadratic iterative algorithm, and the proposed optimization procedure enables precise characterization of resolution and noise properties.

5. S. S. Stone, J. P. Haldar, S. C. Tsao, W.-M. W. Hwu, Z.-P. Liang, B. P. Sutton.
Accelerating Advanced MRI Reconstructions on GPUs.
ACM Computing Frontiers, Ischia, 2008, pp. 261-272.

GPUs can make advanced magnetic resonance imaging (MRI) reconstruction algorithms attractive in clinical settings, thereby improving the quality of MR images across a broad spectrum of applications. At present, MR imaging is often limited by high noise levels, significant imaging artifacts, and/or long data acquisition (scan) times. Advanced image reconstruction algorithms can mitigate these limitations and improve image quality by simultaneously operating on scan data acquired with arbitrary trajectories and incorporating additional information such as anatomical constraints. However, the improvements in image quality come at the expense of a considerable increase in computation.
This paper describes the acceleration of an advanced reconstruction algorithm on NVIDIA's Quadro FX 5600. Optimizations such as register allocating the voxel data, tiling the scan data, and storing the scan data in the Quadro's constant memory dramatically reduce the reconstruction's required bandwidth to on-chip memory. The Quadro's special functional units provide substantial acceleration of the trigonometric computations in the algorithm's inner loops, and experimentally-tuned code transformations increase the reconstruction's performance by an additional 20%.
The reconstruction of a 3D image with 128^3 voxels ultimately achieves 150 GFLOPS and requires less than two minutes on the Quadro, while reconstruction on a quad-core CPU is thirteen times slower. Furthermore, relative to the true image, the error exhibited by the advanced reconstruction is only 12%, while conventional reconstruction techniques incur error of 42%. In short, the acceleration afforded by the GPU greatly increases the appeal of the advanced reconstruction for clinical MRI applications.

6. J. P. Haldar, V. J. Wedeen, M. Nezamzadeh, G. Dai, N. Schuff, Z.-P. Liang.
Improved SNR in Diffusion Spectrum Imaging with Statistical Reconstruction.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 141. (Abstract)

Diffusion spectrum imaging (DSI) is a powerful technique for the characterization of complex tissue microarchitecture. However, the potential of this technique has not been fully utilized for high-resolution biological studies because of long acquisition times and limited signal-to-noise ratio. This paper presents a new approach for reconstructing DSI images, using a statistical model that takes advantage of the high level of spatial-spectral correlation in DSI images. This method can provide significant improvements in signal-to-noise ratio relative to conventional techniques, revealing additional structures in DSI data which have previously been hidden by noise.

7. J. P. Haldar, D. Hernando, D. C. Karampinos, B. P. Sutton, J. G. Georgiadis, Z.-P. Liang.
Sensitivity Encoding of Chemical Shifts.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 1283. (Abstract)

Conventional spectroscopic imaging experiments acquire multiple temporal encodings to enable the separation of different resonance frequencies. In this work, we explore a new kind of spectroscopic imaging that requires only a single temporal encoding, relying instead on the sensitivity encoding provided by an array of receiver coils. This provides a single-shot mechanism for chemical shift artifact correction and spectroscopic signal separation, although this comes at the expense of significant noise sensitivity.

8. J. P. Haldar, S. S. Stone, H. Yi, S. C. Tsao, B. P. Sutton, W.-M. W. Hwu, Z.-P. Liang.
Fast MR Image Reconstruction using Graphics Processing Units.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 1493. (Abstract)

Advanced algorithms for image reconstruction are becoming increasingly common, but their utility is limited by computational requirements. In this work, we show that significant improvements in reconstruction speed can be achieved by performing data-parallel computations on graphics processing units (GPUs). Specifically, we leverage the resources of a single NVIDIA GeForce 8800 GTX to achieve computational performance of more than 150 GFLOPS, hundreds of times faster than what is reported on a single modern central processing unit (CPU).

9. I. C. Atkinson, K. R. Thulborn, A. Lu, J. Haldar, X. J. Zhou, T. Claiborne, Z.-P. Liang.
Quantitative 23-Sodium and 17-Oxygen MR Imaging in Human Brain at 9.4 Tesla Enhanced by Constrained k-Space Reconstruction.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 335. (Abstract)

The sensitivity of ultra-high field MRI enables quantitative imaging of non-proton species such as 23-sodium and 17-oxygen. Constrained k-space reconstruction techniques can be used to improve the spatial resolution of the acquired data without compromising the ability to quantify the final image. This approach of enhanced image reconstruction combined with the improved sensitivity of high field broadens the human applications of metabolic MR imaging by minimizing otherwise long acquisition times to achieve adequate spatial resolution for the anatomy and SNR performance for quantification.

10. D. Hernando, J. Haldar, L. Ying, K. King, D. Xu, Z.-P. Liang.
Interventional MRI with Sparse Sampling: An Application of Compressed Sensing.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 1482. (Abstract)

Interventional MRI (I-MRI) is an important dynamic imaging application, allowing the guidance of therapeutic procedures, which requires high frame-rate and near-real-time reconstruction. Compressed sensing (CS) allows high-resolution reconstruction from a reduced number of samples by exploiting the sparsity of the signal. In this work, CS is tailored to maximize the sparsity in each frame while satisfying the inherent causality constraints in I-MRI reconstruction, so that high-quality images can be obtained from a small number of samples.

11. D. Hernando, P. Kellman, J. Haldar, Z.-P. Liang.
Estimation of Water/Fat Images, B0 Field Map and T2* Map using VARPRO.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 1517. (Abstract)

T2* estimation in Dixon imaging is important for obtaining accurate water/fat intensity estimates when the relaxation effect cannot be neglected. Moreover, the T2* map can have diagnostic value of its own. Here we present a method for estimating B0- and T2*-maps along with water/fat images from Dixon acquisitions, by extending a recently proposed variable projection method. This method provides accurate estimates regardless of the nonconvexity of the corresponding estimation problem. Furthermore, an efficient approximate algorithm is derived based on Cramer-Rao bound analysis. The performance of the proposed methods has been validated using cardiac imaging data.

12. D. Hernando, P. Kellman, J. Haldar, Z.-P. Liang.
Improved Field Map Estimation in the Presence of Multiple Spectral Components.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 3054. (Abstract)

B0 field map estimation in the presence of multiple spectral components is an important and challenging problem in MRI, e.g., for cardiac and abdominal imaging, where the B0 field may contain large variations across the image. This paper presents a novel method for regularized field map estimation, which formulates the estimation of the complete field map as a joint problem (instead of, e.g., voxel-by-voxel estimation followed by smoothing). In vivo cardiac results demonstrate good robustness of the proposed method.

13. J. H. Kim, J. Haldar, Z.-P. Liang, S.-K. Song.
Actively Decoupled Two Coil System Enables in Vivo DTI of Mouse Cervical Spinal Cord at 4.7 T.
International Society for Magnetic Resonance in Medicine 16th Scientific Meeting, Toronto, 2008, p. 2304. (Abstract)

In vivo DTI was performed for mouse cervical spinal cord at a 4.7 T magnet. Actively decoupled volume coil (RF excitation) and saddle type surface coil (signal receiver) provided good SNR to perform in vivo DTI within one hour using the conventional spin echo diffusion weighted imaging sequence. The acquired DTI maps revealed anisotropic characteristics of white matter and dorsal gray matter. Also, the coherent, axially elongated axonal fiber tracts can easily be seen with diffusion ellipsoids. The present results showed feasibility of in vivo diffusion observation of mouse cervical spinal cord at 4.7 T with reduced scan time.

#### 2007

1. K. R. Thulborn, I. C. Atkinson, A. Lu, T. Claiborne, M. P. Flannery, X. J. Zhou, J. Haldar, Z.-P. Liang.
Metabolic MR Imaging of Human Brains at 9.4 Tesla.
6th Bi-Annual Minnesota Workshops on High Field MR Imaging and Spectroscopy and MR Imaging of Brain Function, Minneapolis, 2007. (Abstract)
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The increased sensitivity of the 9.4 Tesla scanner for human brain imaging developed and funding by the University of Illinois has allowed access to non-proton signals for high quality MR imaging. New opportunities now exist for metabolic imaging of humans.
Because the field strength of 9.4 Tesla exceeds the upper limit of the current FDA guidelines for static magnetic field exposure for humans, safety testing under IDE with IRB approval has been performed. Measurements of vital signs (heart rate, respiratory rate, peripheral arterial oxygen saturation, skin temperature, end tidal CO2 levels and ECG) and cognitive performance before and after exposure to 9.4 Tesla for 60 minutes during quantitative twisted projection sodium imaging of the brain demonstrate no statistically significant changes in humans (n=25). The specific absorption rate (SAR) of RF power for quantitative sodium imaging did not surpass 50% of FDA guidelines and, at 105 MHz, the power deposition was reasonably uniform with our current volume coils.
23-Sodium images of human brain at 3.125 x 3.125 x 3.125 mm3 resolution acquired in 7 minutes and 48 seconds, have been quantified as tissue sodium concentration (TSC) maps and match literature values obtained at lower resolution with longer acquisition times. The approach has been extended to acquire natural abundance17-oxygen (0.037%) water images of the human brain at 54 MHz. Although sensitivity and concentration are lower for the17-oxygen signal, images with 7.4 x 7.4 x 7.4 mm3 resolution can be obtained in 7 minutes and 50 seconds without exceeding SAR limits (<65%). By maximizing acquisition efficiency, natural abundance 17-oxygen image of the human brain can be obtained in 47 seconds. These images can be enhanced with anatomically constrained k-space reconstruction of the 17-oxygen-labeled water images using the higher resolution co-registered 23-sodium images. The errors of quantification in this approach are under investigation. Enrichment techniques are also being developed to further enhance sensitivity.
The 9.4 Tesla scanner has been in operation for 3 years and demonstrated excellent Bo stability (< 2Hz/day) and cryogen boil off rates within specifications (<0.3liters/hr). The water-cooled head gradient set and power amplifier system has demonstrated excellent gradient fidelity (<0.07%, as measured by the accuracy of k-space trajectory) and mechanical stability over this time using demanding but "compassionate" twisted projection imaging. The wider clear bore magnet (80 cm clear bore diameter) together with the torque-balanced asymmetric gradient set allows easy head and shoulder access for humans. This space is readily appreciated by human subjects familiar with the more restricted access of lower field clinical scanners (60cm). Given the ongoing developments of imaging signals at other non-proton frequencies, such as 31P, metabolic imaging in humans promises to realize new investigations of the human brain in health and disease.

2. S. S. Stone, H. Yi, J. P. Haldar, W.-M. W. Hwu, B. P. Sutton, Z.-P. Liang.
How GPUs Can Improve the Quality of Magnetic Resonance Imaging.
The First Workshop on General Purpose Processing on Graphics Processing Units, Boston, 2007.

In magnetic resonance imaging (MRI), non-Cartesian scan trajectories are advantageous in a wide variety of emerging applications. Advanced reconstruction algorithms that operate directly on non-Cartesian scan data using optimality criteria such as least-squares (LS) can produce significantly better images than conventional algorithms that apply a fast Fourier transform (FFT) after interpolating the scan data onto a Cartesian grid. However, advanced LS reconstructions require significantly more computation than conventional reconstructions based on the FFT. For example, one LS algorithm requires nearly six hours to reconstruct a single three-dimensional image on a modern CPU. Our work demonstrates that this advanced reconstruction can be performed quickly and efficiently on a modern GPU, with the reconstruction of a 643 3D image requiring just three minutes, an acceptable latency for key applications.
This paper describes how the reconstruction algorithm leverages the resources of the GeForce 8800 GTX (G80) to achieve over 150 GFLOPS in performance. We find that the combination of tiling the data and storing the data in the G80's constant memory dramatically reduces the algorithm's required bandwidth to off-chip memory. The G80's special functional units provide substantial acceleration for the trigonometric computations in the algorithm's inner loops. Finally, experiment-driven code transformations increase the reconstruction's performance by as much as 60% to 80%.

3. C. L. Shaffer, D. Hernando, J. Stastny, S. Kalyanam, J. Haldar, E. Chaney, X. Liang, M. F. Insana.
Multimodality Imaging Development Using 3D Gel Cultures.
Biomedical Engineering Society Annual Fall Meeting, Los Angeles, 2007, p. 374. (Abstract)
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Three dimensional (3D) cell culture gels are invaluable tools for isolating complex molecular processes associated with cancer. We are developing 3D gels for studying multimodality diagnostic imaging of structural and functional features of malignant breast disease. Our first study involves EHS extracellular matrix extract (Matrigel, BD Biosciences) for viewing fibroblast cell proliferation in a controlled and well characterized microenvironment. These gels were studied by combining mechanical, optical, and magnetic resonance spectroscopic imaging (MRSI) techniques to describe stromal structure (mechanical), cell distribution and phenotype (optical), and metabolic effects (pH imaging via MRSI). After 4 days of culture in the 3D gel, a 5-fold increase in fibroblast number was observed with optical coherence tomography and histology. Using imidazole as an exogenous pH indicator, MRSI showed the cell proliferation reduced gel pH by 0.2. A concomitant increase in collagen production stiffened the gel 65%; the elastic modulus increased 268 Pa. The observed non-uniform cell migration patterns were consistent with the multimodality image data, confirming that diagnostic images can describe essential functional and structural properties. Adding normal and cancerous epithelial cells, the effects of heterotypic cell signaling essential for tumor development can be imaged. Because they create known cellular microenvironments characteristic of molecular disease, 3D gels form "living phantoms" for detailed multimodality imaging studies of cancer.

4. J. P. Haldar, Z.-P. Liang.
High-Resolution Diffusion MRI.
29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Lyon, 2007, pp. 311-314.
EMBS Student Paper Competition Geographic Finalist: North America.

This paper presents a magnetic resonance imaging method that can provide high-resolution images characterizing water diffusion in biological tissues. These images contain information about tissue microstructure, thereby providing a useful means to monitor physiological changes. The proposed method overcomes the long-standing problem of limited signal-to-noise ratio with diffusion MRI by using penalized maximum-likelihood reconstruction. Experiments performed on a mouse brain illustrate the ability of the technique to elucidate high resolution structural detail that would not be visible using other non-invasive approaches.

5. J. P. Haldar, D. Hernando, M. D. Budde, Q. Wang, S.-K. Song, Z.-P. Liang.
High-Resolution MR Metabolic Imaging.
29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Lyon, 2007, pp. 4324-4326.
Invited Presentation.

Magnetic resonance spectroscopic imaging has been recognized for a long time as a powerful tool for biochemical imaging. However, its practical utility is still rather limited due to poor spatial resolution, low signal-to-noise ratio, and long data acquisition times. In this work, we propose a new technique that enables reconstruction of metabolite maps with high spatial resolution. This technique uses a statistical model to incorporate known anatomical boundaries for edge-preserving noise filtering. This statistical reconstruction scheme makes it possible to use very noisy data, thereby enabling the collection of high-resolution data in a reasonable amount of time. We illustrate the performance of this method with images of the N-acetyl-L-aspartate distribution from an in vivo mouse brain.

6. J. P. Haldar, J. Anderson, S.-W. Sun.
Maximum Likelihood Estimation of T1 Relaxation Parameters Using VARPRO.
Joint Annual Meeting ISMRM-ESMRMB, Berlin, 2007, p. 41. (Abstract)

Nonlinear least-squares curve fitting algorithms are often employed to find maximum likelihood estimates of T1 relaxation parameters. However, the specific nonlinear least-squares cost function can be poorly behaved, and in high noise situations, can provide answers without strong physical meaning. By using the VARPRO algorithm to reduce the dimensionality of the nonlinear least-squares problem, we are able to solve the optimization problem efficiently and noniteratively, and study its structure. Insights gained from this analysis provide meaningful ways of incorporating prior information into the reconstruction process, which is particularly useful when the standard nonlinear least-squares approach gives unsatisfactory results.

7. J. P. Haldar, D. Hernando, B. P. Sutton, Z.-P. Liang.
Data Acquisition Considerations for Compressed Sensing in MRI.
Joint Annual Meeting ISMRM-ESMRMB, Berlin, 2007, p. 829. (Abstract)

Compressed sensing (CS) has drawn significant attention in the signal processing community due to the surprising result that if an unknown signal is known to be compressible, then near-optimal reconstruction is often possible given a small set of measurements. The CS methodology has shown promising application in MRI, with data samples collected quasi-randomly in k-space. In this work, we present a systematic evaluation of different encoding schemes for CS-MRI in the presence of noise, and compare the results with more traditional MR reconstruction approaches.

8. J. P. Haldar, D. Hernando, M. D. Budde, Q. Wang, S.-K. Song, Z.-P. Liang.
High-Resolution Spectroscopic Imaging with Statistical Reconstruction.
Joint Annual Meeting ISMRM-ESMRMB, Berlin, 2007, p. 1231. (Abstract)

This paper proposes a new scheme for spectroscopic imaging. In contrast to conventional methods that only collect low frequency k-space data to limit noise in the reconstruction, the new method enables extended k-space coverage to achieve high spatial resolution. It is shown that the loss of signal-to-noise ratio associated with the new data acquisition scheme can be effectively mitigated by using statistical modeling in concert with anatomical prior information. Simulation and experimental results illustrate the resolution which is possible using these techniques.

9. J. P. Haldar, D. Hernando, Z.-P. Liang.
Estimation of Compartmental Signals from Limited Fourier Samples.
Joint Annual Meeting ISMRM-ESMRMB, Berlin, 2007, p. 1910. (Abstract)

In many imaging applications, the goal is to generate summary statistics regarding the behavior of the signal within given regions of interest, e.g., to compare the average signal from normal-appearing and pathological tissues. In this work, we show that it is possible to generate better estimates of these compartmental signals without going through an image reconstruction step. This is particularly advantageous for experiments where a small number of measured data is collected.

10. D. Hernando, J. Haldar, B. Sutton, Z-P. Liang.
Removal of Lipid Nuisance Signals in MRSI Using Spatial-Spectral Constraints.
Joint Annual Meeting ISMRM-ESMRMB, Berlin, 2007, p. 1244. (Abstract)

Analysis and quantification of MRSI data is made more difficult by the presence of lipid nuisance signals in the spectra, which appear as broad and distorted peaks overlapping several metabolites of interest. We introduce a method that incorporates spatial and spectral constraints for effective estimation and removal of lipid signals in MRSI. The proposed method has been tested with both phantom andbiological MRSI data.

11. D. Hernando, J. Haldar, J. Ma, Z.-P. Liang.
A Linear Prediction Approach to Joint Estimation of Water/Fat Images and Field Inhomogeneity Map.
Joint Annual Meeting ISMRM-ESMRMB, Berlin, 2007, p. 1629. (Abstract)

Three-point Dixon methods allow the determination of water and fat images, as well as estimation of the field inhomogeneity map. Here we present an efficient, noniterative method for joint estimation of the water/fat images and field map based on linear prediction. The method is demonstrated on a set of images acquired using the IDEAL echo spacings. A theoretical analysis is also provided for determination of acquisition parameters to minimize the error in noisy conditions.

12. J. P. Haldar, D. Hernando, Z.-P. Liang.
Shaping Spatial Response Functions for Optimal Estimation of Compartmental Signals from Limited Fourier Data.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, 2007, pp. 1364-1367.

The goal of quantitative MRI experiments is often to generate summary statistics regarding the behavior of the image within given regions of interest. In this work, we show that it is possible to generate better estimates for compartmental signals without requiring an initial image reconstruction step. The proposed approach is optimal in that it minimizes the worst case mean-squared error for the class of linear estimators and for a set of signals satisfying known magnitude constraints. In addition, it conveniently results in a criterion by which different experimental parameters can be compared. The extension of this region of interest quantification to image reconstruction is straightforward, as image reconstruction can be thought of as a graphical tiling of region of interest estimates of the signal.

13. D. Hernando, J. Haldar, B. Sutton, Z.-P. Liang.
Removal of Lipid Signal in MRSI Using Spatial-Spectral Constraints.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, 2007, pp. 1360-1363.

Analysis and quantification of magnetic resonance spectroscopic imaging data is complicated by the presence of lipid nuisance signals. These signals typically appear as peaks with amplitudes much larger than those of the metabolites of interest and, in the case of lipids, present broad, distorted lineshapes. This paper introduces a method that incorporates constraints in both the spatial and spectral domains for improved removal of lipid signals. Specifically, this method uses an anatomical image of the lipid locations to spatially constrain the lipid estimate as well as a field inhomogeneity map to improve spectral fitting of the lipid lineshape. Experimental results are provided to demonstrate the performance of the proposed method.

#### 2006

1. J. P. Haldar, M. Jacob, A. Ebel, X. Zhu, N. Schuff, D. Hernando, B. Sutton, Z.-P. Liang.
Constrained Spectroscopic Imaging with Hard and Soft Anatomical Boundary Constraints.
International Society for Magnetic Resonance in Medicine 14th Scientific Meeting, Seattle, 2006, p. 3077. (Abstract)

This paper addresses an outstanding problem in MRSI, i.e., the inversion of noisy, limited Fourier data with anatomical constraints. The proposed method incorporates exact boundary constraints into the basis functions of a spatial-spectral model, and uncertain boundary constraints into a regularizing penalty function. The final reconstruction is obtained by solving a convex optimization problem. By providing an effective way to integrate anatomical images with spectroscopic images, the proposed method can yield higher-resolution metabolite maps than conventional methods.

2. M. Jacob, B. P. Sutton, J. Haldar, Z.-P. Liang.
Improved Spectroscopic Imaging using Echo-Planar Scans and Sparse Reconstruction.
International Society for Magnetic Resonance in Medicine 14th Scientific Meeting, Seattle, 2006, p. 2964. (Abstract)

We find that the model based spectroscopic imaging framework, originally derived for reduced encoding, is more appropriate for fast-scan techniques; these schemes can provide larger k-space coverage in the same scan time as the reduced phase encoding case. This enables us to redesign the model-based framework to these schemes, thus simultaneously achieving high spatial resolution, signal to noise ratio, and low artifacts. We then present a data-adaptive basis selection procedure to rectify some of the problems associated with the current model based techniques. To achieve this goal, we propose to specify the basis functions using linear constraints. We start with a rigid image model, formulated in this framework. We then relax some of its constraints based on the MRSI data. This enables us to make the model flexible, without losing its robustness.

3. J. P. Haldar, M. Jacob, A. Ebel, X. Zhu, N. Schuff, D. Hernando, B. Sutton, Z.-P. Liang.
Regularized Inversion of Noisy, Incomplete MR Spectroscopic Imaging Data with Anatomical Prior.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, 2006, pp. 718-721.

This paper addresses the image reconstruction problem in MR spectroscopic imaging experiments where noisy, limited Fourier data are often collected due to temporal constraints. A parametric method is proposed which is capable of incorporating exact and uncertain boundary information. Experimental results show that the technique can generate metabolic images with much higher spatial resolution than the conventional Fourier method and existing constrained reconstruction methods.

4. D. Hernando, J. Haldar, Z.-P. Liang.
Reduced-Encoding MRI Using Higher-Order Generalized Series.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, 2006, pp. 29-32.

Reduced-encoding MRI has been used in a wide variety of MR applications where temporal resolution is critical. Although the Generalized Series model (with basis functions constructed from a reference image) allows the reconstruction of high-resolution dynamic images from a small number of encodings, the ability of the model to capture localized dynamic features is limited by the model order, which in the past has been set equal to the number of encodings acquired. This paper extends this model by incorporating higher frequency terms, which allows for a sharper reconstruction of new localized features. Since the series coefficients of the higher-order model are underdetermined by the data collected, two important issues arise which are addressed in this paper: the definition of an appropriate regularization criterion and the solution of the corresponding optimization problem. Results from simulated as well as biological data are also provided to demonstrate the properties of this model.

5. M. Jacob, B. Sutton, J. Haldar, Z.-P. Liang.
On Model-Based MR Spectroscopic Imaging.
IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, 2006, pp. 726-729.

In this paper, we analyze the model-based reconstruction framework in MR spectroscopic imaging and derive an exact expression for the reconstruction error. Based on the insight provided by the analysis, we propose two modifications: (a) we introduce a new echo-planar imaging sequence to acquire more Fourier samples in the same scan duration, since increasing the number of Fourier samples will decrease the bias in the reconstructions. We then use the model-based framework to effectively compensate for the corresponding loss in signal to noise ratio/measurement, (b) we observe that model misfit can affect the reconstructions in constrained imaging much more seriously than standard Fourier reconstruction. We propose a data adaptive basis selection procedure to reduce the misfit, without significantly increasing the noise variance. Both these improvements together enable high-resolution reconstructions that are more robust and with fewer artifacts as compared to reduced encoding, without increasing the scan time.

#### 2005

1. L. Ying, J. Haldar, Z.-P. Liang.
An Efficient Non-Iterative Reconstruction Algorithm for Parallel MRI with Arbitrary K-Space Trajectories.
27th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Shanghai, 2005, pp. 1344-1347.

Parallel imaging using multiple receiver coils has emerged as an effective tool to reduce imaging time in various MRI applications. Although several different image reconstruction methods have been developed and demonstrated to be successful for Cartesian k-space trajectories, there is a lack of efficient reconstruction methods for arbitrary trajectories. In this paper, we formulate the reconstruction problem in k-space and propose a novel image reconstruction method that is fast and effective for arbitrary trajectories. To obtain the desired image, the method reconstructs the Nyquist-sampled k-space data of the image on a uniform Cartesian grid from the undersampled multichannel k-space data on an arbitrary grid, followed by inverse Fourier transform. We demonstrate the effectiveness of the proposed fast algorithm using simulations. In particular, we compare the proposed method with the existing iterative method and show that the former is able to achieve similar image quality to the latter but with reduced computational complexity.

2. J. P. Haldar, L. Ying, Z.-P. Liang.
Lattice Sampling of k-Space for Parallel Imaging.
International Society for Magnetic Resonance in Medicine 13th Scientific Meeting, Miami, 2005, p. 2420. (Abstract)

SENSE reconstruction from arbitrary k-space trajectories can be very slow. This paper proposes a new class of sampling trajectories that admit fast solution of the reconstruction problem. Specifically, lattice or composite lattice trajectories are shown to have sparse point spread functions, so the number of aliasing image values in the Fourier transform of an undersampled lattice is small. Image reconstruction is performed by inverting a sparse matrix, which can be done quickly. The paper also successfully solves the SENSE reconstruction problem for zig-zag EPI trajectories, in which the proposed algorithm shows a significant speed increase compared to the conventional methods.

### Thesis/Dissertation

• J. P. Haldar.
Constrained Imaging: Denoising and Sparse Sampling.
Ph.D. Dissertation, University of Illinois at Urbana-Champaign, May 2011.

Magnetic resonance imaging (MRI) is a powerful tool for studying the anatomy, physiology, and metabolism of biological systems. Despite the fact that MRI was introduced decades ago and has already revolutionized medical imaging, current applications are still far from utilizing the full potential of the MR signal. Traditional MRI data acquisition and image reconstruction methods are based on simple Fourier inversion, leading to undesirable trade-offs between image resolution, signal-to-noise ratio (SNR), and data acquisition time. Classical approaches to addressing these trade-offs have relied on improved imaging hardware and more efficient pulse sequences. In contrast, our work addresses the limitations of MR using relatively less-explored signal processing approaches, which have recently become practical because of increasing computational capabilities. This dissertation concerns the use of constrained imaging models to guide the design of both data acquisition and image reconstruction, leading to improved imaging performance in the context of both noise-limited and resolution-limited scenarios.
To address noise limitations for high-resolution imaging, we introduce a quasi-Bayesian edge-preserving smoothness prior for modeling correlated image sequences. The prior models the correlated edge structures that are observed in the image sequence, and is used within a penalized maximum likelihood framework to reduce image noise while preserving high-resolution anatomical structure. In contrast to many constrained imaging methods, we demonstrate that the proposed method is relatively simple to analyze and is robust to model inaccuracy when reconstruction parameters are chosen appropriately. Resolution and SNR analysis shows that the proposed formulations lead to substantial improvements in SNR with only a moderate decrease in spatial resolution. An examination of resolution and SNR trade-offs is presented, which serves as a guide for the optimal design of data acquisition and image reconstruction procedures in this context.
To address limited spatial resolution in high-SNR scenarios, we design specialized data acquisition and image reconstruction procedures to enable image reconstruction from sparsely-sampled data. Specifically, we leverage prior information that the image has sparse or low-rank structure to significantly reduce sampling requirements in two different contexts. In the first context, we assume that the image is sparse in a known transform domain, and develop a novel non-Fourier data acquisition scheme to enable high-quality reconstruction from undersampled data. The second context is specific to spatiotemporal imaging, and it is assumed that the temporal evolution of the spatiotemporal image is highly correlated at different spatial positions. This correlation leads to the formulation of a novel low-rank matrix recovery problem, which we demonstrate can be solved efficiently and effectively using special algorithms.
Applications of the proposed techniques are illustrated with simulated and experimental data from a variety of different MR imaging scenarios.

• J. P. Haldar.
Sparse Matrix Formulations for Fast Image Reconstruction in Multichannel MRI.
M.S. Thesis, University of Illinois at Urbana-Champaign, August 2005.
[toggle abstract]

Multichannel data acquisition is a powerful technique that can greatly increase the speed of magnetic resonance imaging (MRI). By collecting information simultaneously from a phased array of receiver coils, multichannel MRI allows shorter acquisition-time requirements than traditional single-coil MRI. While data collection can be significantly faster for multichannel experiments, this often comes at the cost of increased computation time, which limits the practical utility of the technique.
The research presented in this thesis is aimed at improving the computational efficiency of phased-array image reconstruction. This thesis addresses two separate questions: (1) How can the data sampling trajectory be used to increase computational speed? (2) How can the properties of the receiver coils be used to produce images more quickly? This thesis shows that, by invoking the properties of the sampling trajectory or the receiver coils, the large full matrices in the imaging equations can be well approximated by sparse matrices, and the resulting equations are very fast to invert. Simulation and experimental results are provided to demonstrate the application of the proposed techniques.

### Patents

• J. P. Haldar, D. Kim.
Diffusion-relaxation correlation spectroscopic imaging.
Provisional US Patent 62/503,836, US patent application number 15/976,548.
• B. Zhao, J. P. Haldar, L. L. Wald.
Systems and Methods for Designing Magnetic Resonance Fingerprinting Imaging Parameters.
US Patent No. 10,241,173.
• J. P. Haldar, R. M. Leahy.
Linear Transform Approach for Processing Diffusion Magnetic Resonance Imaging Data.
US Patent No. 9,880,246.