## Justin P. Haldar: Publications

### Journal Publications

#### 2013

1. 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 2013, In Press.

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.

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.

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.

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.

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.

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. 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.

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.

#### 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.

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] [sample Matlab code]

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.

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. 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.

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

#### 2013

1. 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.

2. 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.

3. 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.

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.

4. 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.
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.

5. D. W. Shattuck, A. A. Joshi, J. P. Haldar, C. Bhushan, S. Lee, 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.

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.

6. 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.

7. 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.

8. 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.

#### 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.
[toggle abstract]

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.
Recipient of the 1st place MIC student paper award.
[toggle abstract]

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.
[toggle abstract]

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.

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.

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.
[toggle abstract]

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.
[toggle abstract]

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.

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.

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.

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.

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.

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.

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.

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.

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.
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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.
[toggle abstract]

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.
[toggle abstract]

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

### Patent

• J. P. Haldar, R. M. Leahy.
Linear Transform Approach for Processing Diffusion Magnetic Resonance Imaging Data.
Provisional US Patent 61/596,643.