Charles Millard^{1,2}, Aaron T Hess^{2}, Boris MailhÃ©^{3}, and Jared Tanner^{1}

^{1}Mathematical Institute, University of Oxford, Oxford, United Kingdom, ^{2}Oxford Centre for Clinical Magnetic Resonance, University of Oxford, Oxford, United Kingdom, ^{3}Siemens Healthineers, Princeton, NJ, United States

We consider two algorithmic challenges for the compressed sensing MRI community: (1) the difficulty of tuning free model parameters and (2) the need to converge quickly. The authors have developed a parameter-free approach to reconstruction which accommodates structurally rich regularizers that can be automatically adapted to near-optimality, removing the need for manual adjustment between images or sampling schemes. We evaluate the algorithm’s performance on three test images of varying type and dimension and find that it converges faster and to a lower mean-squared error than its competitors, even when they are optimally tuned.

A second limiting factor for the clinical utility of compressed sensing MRI is the computational expense of reconstruction algorithms. For high-dimensional problems it may not be feasible to run an algorithm until convergence, which can limit the quality of reconstruction.

In response to these challenges, the authors recently developed the Variable Density Approximate Message Passing (VDAMP) algorithm for parameter-free compressed sensing MRI

1. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magnetic Resonance in Medicine, vol. 58, pp. 1182–1195, 12 2007.

2. A. Hsiao, M. Lustig, M. T. Alley, M. Murphy, F. P. Chan, R. J. Herfkens, and S. S. Vasanawala, “Rapid Pediatric Cardiac Assessment of Flow and Ventricular Volume With Compressed Sensing Parallel Imaging Volumetric Cine Phase-Contrast MRI,” American Journal of Roentgenology, vol. 198, pp. W250–W259, 3 2012.

3. K. G. Hollingsworth, D. M. Higgins, M. McCallum, L. Ward, A. Coombs, and V. Straub, “Investigating the quantitative fidelity of prospectively undersampled chemical shift imaging in muscular dystrophy with compressed sensing and parallel imaging reconstruction,” Magnetic Resonance in Medicine, vol. 72, pp. 1610–1619, 12 2014.

4. O. N. Jaspan, R. Fleysher, and M. L. Lipton, “Compressed sensing MRI: a review of the clinical literature,” The British Journal of Radiology, vol. 88, p. 20150487, 12 2015.

5. K. Khare, C. J. Hardy, K. F. King, P. A. Turski, and L. Marinelli, “Accelerated MR imaging using compressive sensing with no free parameters,” Magnetic Resonance in Medicine, vol. 68, pp. 1450–1457, 11 2012.

6. F. Ong, M. Uecker, U. Tariq, A. Hsiao, M. T. Alley, S. S. Vasanawala, and M. Lustig, “Robust 4D Flow Denoising Using Divergence-Free Wavelet Transform,” Magnetic resonance in medicine: official journal of the Society of Magnetic Resonance in Medicine/ Society of Magnetic Resonance in Medicine, vol. 73, p. 828, 2 2015.

7. C. M. Stein, “Estimation of the Mean of a Multivariate Normal Distribution,” The Annals of Statistics, vol. 9, pp. 1135–1151, 11 1981.

8. C. Millard, A. T. Hess, B. Mailhe, and J. Tanner, “An
Approximate Message Passing Algorithm for Rapid Parameter-Free Compressed
Sensing MRI,” 11 2019. [Online] https://arxiv.org/abs/1911.01234

9. D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, pp. 18914–9, 11 2009.

10. A. Beck and M. Teboulle, “A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems,” SIAM Journal on Imaging Sciences, vol. 2, pp. 183–202, 1 2009.

11. D. L. Donoho and I. M. Johnstone, “Adapting to Unknown Smoothness via Wavelet Shrinkage,” Journal of the American Statistical Association, vol. 90, pp. 1200–1224, 121995.