Low-rank optimization algorithm for accelerated dynamic MRI

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In this paper, we propose a low rank optimization algorithm to reconstruct under-sampled dynamic MRI, which consists of finding a matrix of minimum rank subject to linear equality constraints. In order to solve this unconstrained nonsmooth convex optimization problem, we develop a fast alternating direction method that uses the nuclear-norm to enforce low-rank constraint. In its Lagrangian form, this is solved through an accelerated proximal gradient (gradient step plus proximal step for nuclear norm) algorithm. Numerical experiments on simulated dataset show encouraging results with low computational time, even at high acceleration rate.