Low-Rank + Sparse (L+S) Reconstruction for Accelerated Dynamic MRI with Separation of Background and Dynamic Components

摘要

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‖_* + 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 l_1-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.