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Learning the sparsity basis in low-rank plus sparse model for dynamic MRI reconstruction

Modeling a temporal image sequence as a super-position of sparse and low-rank component stems from studies in principal component pursuit (PCP). Recently this technique was applied for dynamic MRI reconstruction with two modifications. First, unlike the original PCP, the problem was to recover the image sequence from under-sampled measurements. Second, the sparse component of the signal was not sparse in itself but in a transform domain. Recent studies in dynamic MRI reconstruction showed that, instead of using a fixed sparsity basis, better recovery results can be achieved when the sparsifying dictionary is adaptively learned from the data using Blind Compressed Sensing (BCS) framework. In this work, we demonstrate that learning the sparsity basis using BCS like techniques improve the recovery accuracy from PCP when applied to dynamic MRI reconstruction problems.