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We introduce a fast iterative non-local shrinkage algorithm to recover MRIdata from undersampled Fourier measurements. This approach is enabled by thereformulation of current non-local schemes as an alternating algorithm tominimize a global criterion. The proposed algorithm alternates between anon-local shrinkage step and a quadratic subproblem. We derive analyticalshrinkage rules for several penalties that are relevant in non-localregularization. The redundancy in the searches used to evaluate the shrinkagesteps are exploited using filtering operations. The resulting algorithm isobserved to be considerably faster than current alternating non-localalgorithms. The comparisons of the proposed scheme with state-of-the-artregularization schemes show a considerable reduction in alias artifacts andpreservation of edges.

Iterative Non-Local Shrinkage Algorithm for MR Image Reconstruction