Monotone FISTA with Variable Acceleration (MFISTA-VA) for Compressed Sensing MRI

Monotone FISTA with Variable Acceleration (MFISTA-VA) for Compressed Sensing MRI

Marcelo Zibetti, PhD

The four knee reconstructions illustrate the first image of the reconstructed sequence of T-weighted images of MRI problem A. From left: NUFFT gridding of the 6-fold undersampled data (22 spokes per image); MFISTA-VA of the 6-fold undersampled data; NUFFT gridding of the fully sampled data (128 spokes per image); and magnitude of the difference, with intensity amplified tenfold, between MFISTA-VA and fully-sampled gridding.


We are making available the codes and test data used in the IEEE-TCI paper Monotone FISTA with Variable Acceleration for Compressed Sensing Magnetic Resonance Imaging (, authored by Marcelo V. W. Zibetti, Elias S. Helou, Ravinder R. Regatte, and Gabor T. Herman.

The MATLAB codes contain implementation of the proposed MFISTA-VA [1], as well as versions of FISTA [2], MFISTA [3], and OISTA [4], for compressed sensing in magnetic resonance imaging. The codes are comprehensive and ready to apply on low rank, sparse, and low rank plus sparse (L+S) problems [5].

Examples use radial T1ρ knee and liver data from NYUMC. Coil sensitivity maps were obtained using ESPIRiT [6].

The curves above show the cost function Ψ(xk) − Ψ(x*) for MRI problem A.


[1] M. V. W. Zibetti, E. S. Helou, R. R. Regatte, and G. T. Herman, “Monotone FISTA with Variable Acceleration for Compressed Sensing Magnetic Resonance Imaging,” IEEE Trans. Comput. Imaging, vol. submitted, 2018.

[2] A. Beck and M. Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM J. Imaging Sci., vol. 2, no. 1, pp. 183–202, Jan. 2009.

[3] A. Beck and M. Teboulle, Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process., vol. 18, no. 11, pp. 2419–2434, Nov. 2009.

[4] D. Kim and J. A. Fessler, An optimized first-order method for image restoration. IEEE International Conference on Image Processing, 2015, pp. 3675–3679.

[5] R. Otazo, E. Candès, and D. K. Sodickson, Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components. Magn. Reson. Med., vol. 73, no. 3, pp. 1125–1136, Mar. 2015.

[6] M. Uecker et al., ESPIRiT-an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA. Magn. Reson. Med., vol. 71, no. 3, pp. 990–1001, Mar. 2014.

[7] J. A. Fessler, On NUFFT-based gridding for non-Cartesian MRI. J. Magn. Reson., vol. 188, no. 2, pp. 191–195, Oct. 2007


PLEASE NOTE: The software available on this page is provided free of charge and comes without any warranty. CAI²R and the NYU School of Medicine do not take any liability for problems or damage of any kind resulting from the use of the files provided. Operation of the software is solely at the user's own risk. The software developments provided are not medical products and must not be used for making diagnostic decisions.

The software is provided for non-commercial, academic use only. Usage or distribution of the software for commercial purpose is prohibited. All rights belong to the author (Marcelo Zibetti, PhD) and the NYU School of Medicine. If you use the software for academic work, please give credit to the author in publications and cite the related publications.

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Philanthropic Support

We gratefully acknowledge generous support for radiology research at NYU Langone Health from:
• The Big George Foundation
• Bernard and Irene Schwartz

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