Low-rank + sparse (L+S) reconstruction for accelerated dynamic MRI with seperation of background and dynamic components

Ricardo Otazo; Daniel K. Sodickson; Emmanuel J. Candès

doi:10.1117/12.2023359

26 September 2013 Low-rank + sparse (L+S) reconstruction for accelerated dynamic MRI with seperation of background and dynamic components

Ricardo Otazo, Daniel K. Sodickson, Emmanuel J. Candès

Author Affiliations +

Proceedings Volume 8858, Wavelets and Sparsity XV; 88581Z (2013) https://doi.org/10.1117/12.2023359
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

L+S matrix decomposition finds the low-rank (L) and sparse (S) components of a matrix M by solving the following convex optimization problem: min‖L‖_*L+S matrix decomposition finds the low-rank (L) and sparse (S) components of a matrix M by solving the following convex optimization problem: ‖L ‖_* + λ‖S‖₁, subject to M=L+S, where ‖L‖_* is the nuclear-norm or sum of singular values of L and ‖S‖₁ is the 1₁-norm| or sum of absolute values of S. This work presents the application of the L+S decomposition to reconstruct incoherently undersampled dynamic MRI data as a superposition of a slowly or coherently changing background and sparse innovations. Feasibility of the method was tested in several accelerated dynamic MRI experiments including cardiac perfusion, time-resolved peripheral angiography and liver perfusion using Cartesian and radial sampling. The high acceleration and background separation enabled by L+S reconstruction promises to enhance spatial and temporal resolution and to enable background suppression without the need of subtraction or modeling.

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Ricardo Otazo, Daniel K. Sodickson, and Emmanuel J. Candès "Low-rank + sparse (L+S) reconstruction for accelerated dynamic MRI with seperation of background and dynamic components", Proc. SPIE 8858, Wavelets and Sparsity XV, 88581Z (26 September 2013); https://doi.org/10.1117/12.2023359

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