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.

Date Published: 26 September 2013
PDF: 8 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88581Z (26 September 2013); doi: 10.1117/12.2023359

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)