Joint Denoising for Diffusion MRI Magnitude Images

This page provides a precompiled Matlab implementation (“p-code”) of a joint denoising algorithm for magnitude diffusion MRI data. In particular, this code combines the regularized statistical denoising method in [1] with the Rician/Non-Central Chi noise modeling described in [2].

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.
[MRM link] [PubMed Central link] [Preprint link]

D. Varadarajan, J. P. Haldar. A Majorize-Minimize Framework for Rician and Non-Central Chi MR Images. IEEE Transactions on Medical Imaging 2015. In Press.
[IEEE link]

The regularized denoising method from [1] takes advantage of the fact that diffusion MRI images are mostly smooth, but also have edge features that are highly correlated between images acquired with different diffusion encoding parameters. The method described in [1] was designed for joint reconstruction of complex k-space data, in which noise is Gaussian. However, most MRI studies discard the original k-space data, and only save magnitude images (discarding the phase information). Discarding the phase changes the noise distribution, and makes denoising significantly more difficult. The Rician/Non-Central Chi noise modeling described in [2] enables more accurate modeling of the noise in magnitude images.

Illustrative sample results generated with this algorithm are provided below.

Sample Results

The algorithm can be applied to various kinds of diffusion MRI data. Below, we show an example of applying the denoising approach to Diffusion Spectrum Imaging (DSI) human brain data.

The figure demonstrates that the algorithm leads to a significant improvement in signal-to-noise ratio (SNR), at the expense of a small loss in spatial resolution. This kind of SNR improvement significantly enhances quantitative diffusion parameter estimation and tractography. For example, see [1], in addition to:

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.
[PDF link] [Poster (ISMRM Login Required)]
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.
[PDF link]
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.
[PDF link] [E-Poster (ISMRM Login Required)]
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.
[PDF link] [Presentation Video (ISMRM Login Required)]

Discussion

Using this denoising algorithm requires the selection of two different parameters (named xi_factor and lambda_factor in the Matlab function). The optimal choice of these two parameters will depend on the details of the diffusion acquisition (b-values, number of diffusion images, SNR, etc.), and will need to be tuned once for each different diffusion acquisition protocol (images acquired with the same protocol from different subjects should be processed using the same parameter values).

The xi_factor variable determines the edge-preservation characteristics of the algorithm. Smaller values typically yield images with sharper edges, though also can give the images a cartoon-like appearance. The lambda_factor parameter determines the amount of spatial smoothing applied by the algorithm. Larger values lead to improved SNR, at the cost of reduced spatial resolution.

Images demonstrating these trade-offs for a range of parameter values are shown below (data from a single-shell diffusion acquisition with 4 b=0 s/mm² images and 61 b=2500 s/mm² images).

Finally, it is also worth noting that the use of magnitude images instead of complex k-space data leads to significant degradation in the denoising performance and theoretical characterizability of the method [1]. The implementation provided on this page for magnitude images is intended to be used only in cases where complex k-space data is not available. If k-space data can be saved, then the original method described in [1] should be preferred.

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This code is licensed under the CC Attribution-Noncommercial-Share Alike 3.0 License. Please cite at least [1] and [2] if you use this code or its derivatives in your own work.

In no event shall the University of Southern California, the Authors, or the Distributors be liable to any party for direct, indirect, special, incidental, or consequential damages, including lost profits, arising out of the use of this software, its documentation, or any derivatives thereof, even if the authors have been advised of the possibility of such damage. The University of Southern California, the Authors, and the Distributors specifically disclaim any warranties, including, but not limited to, the implied warranties of merchantability, fitness for a particular purpose, and non-infringement. This software is provided on an "as is" basis, and the authors and distributors have no obligation to provide maintenance, support, updates, enhancements, or modifications. This software is for research purposes only and has not been approved for clinical use.

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