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

An accurate, rapidly converging, low-compute algorithm for approximating solutions to the least absolute shrinkage and selection operator (LASSO) problem.

We are making available an algorithm for monotone fast iterative shrinkage-thresholding (MFISTA) with variable acceleration (VA) that reduces reconstruction time of compressed sensing MRI.

Examples NUFFT and MFISTA image reconstructions from undersampled MRI data, NUFFT reconstruction from fully sampled data, and comparison between the fully sampled NUFFT and undersampled MFISTA-VA reconstruction.
Four reconstructions of T-weighted knee MRI. Clockwise from top left: non-uniform fast Fourier transform (NUFFT) gridding of 6-fold undersampled data (22 spokes per image); MFISTA-VA of 6-fold undersampled data; NUFFT gridding of the fully sampled data (128 spokes per image); and the difference—amplified tenfold—between MFISTA-VA and fully-sampled gridding.

The MATLAB codes contain implementation of the proposed MFISTA-VA, as well as versions of FISTA, MFISTA, and OISTA, 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. Examples are given with radial T knee and liver data from NYU Langone Health. Coil sensitivity maps were obtained with ESPIRiT.

For more information, see the related publication and references.

Related Publication

Zibetti MVW, Helou ES, Regatte RR, Herman GT.
Monotone FISTA with Variable Acceleration for Compressed Sensing Magnetic Resonance Imaging.
IEEE Trans Comput Imaging. 2019 Mar;5(1):109-119. doi: 10.1109/TCI.2018.2882681

Please cite this work if you are using MFISTA-VA in your research.


Beck A, Teboulle M.
A fast iterative shrinkage-thresholding algorithm for linear inverse problems.
SIAM J Imaging Sci. 2009;2(1):183-202. doi: 10.1137/080716542

Beck A, Teboulle M.
Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems.
IEEE Trans Image Process. 2009 Jul 24;18(11):2419-34. doi: 10.1109/TIP.2009.2028250

Kim D, Fessler JA.
An optimized first-order method for image restoration.
2015 IEEE International Conference on Image Processing (ICIP). 2015 Sep 27 (pp. 3675-3679). doi: 10.1109/ICIP.2015.7351490

Otazo R, Candès E, Sodickson DK.
Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components.
Magn Reson Med. 2015 Mar;73(3):1125-36. doi: 10.1002/mrm.25240

Uecker M, Lai P, Murphy MJ, Virtue P, Elad M, Pauly JM, Vasanawala SS, Lustig M.
ESPIRiT–an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA.
Magn Reson Med. 2014 Mar;71(3):990-1001. doi: 10.1002/mrm.24751

Fessler JA.
On NUFFT-based gridding for non-Cartesian MRI.
J Magn Reson 2007 Oct;188(2):191-5. doi: 10.1016/j.jmr.2007.06.012

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The software available on this page is provided free of charge and comes without any warranty. CAI²R and NYU Grossman 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 Wust Zibetti) and NYU Grossman School of Medicine. If you use the software for academic work, please give credit to the author in publications and cite the related publications.

Please spell out your affiliation (e.g. “New York University” rather than “NYU”).


Questions about this resource may be directed to Marcelo Wust Zibetti, PhD.