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