Iterative Non-Local Shrinkage Algorithm for MR Image Reconstruction

TL;DR

This paper presents a fast iterative non-local shrinkage algorithm for MRI image reconstruction from undersampled data, improving speed and image quality compared to existing methods.

Contribution

The paper introduces a novel, faster iterative non-local shrinkage algorithm that reformulates non-local schemes as an alternating minimization process with analytical shrinkage rules.

Findings

Significantly faster than existing non-local algorithms.

Reduces alias artifacts in reconstructed images.

Preserves edges effectively in MRI reconstructions.

Abstract

We introduce a fast iterative non-local shrinkage algorithm to recover MRI data from undersampled Fourier measurements. This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a global criterion. The proposed algorithm alternates between a non-local shrinkage step and a quadratic subproblem. We derive analytical shrinkage rules for several penalties that are relevant in non-local regularization. The redundancy in the searches used to evaluate the shrinkage steps are exploited using filtering operations. The resulting algorithm is observed to be considerably faster than current alternating non-local algorithms. The comparisons of the proposed scheme with state-of-the-art regularization schemes show a considerable reduction in alias artifacts and preservation of edges.