Compressed MRI Reconstruction Exploiting a Rotation-Invariant Total Variation Discretization

TL;DR

This paper introduces a rotation-invariant total variation discretization for compressed MRI reconstruction, leveraging a tailored optimization method to improve accuracy and robustness over existing approaches.

Contribution

It presents a novel rotation-invariant total variation functional and adapts the Malitsky-Pock method for constrained MRI reconstruction, outperforming current state-of-the-art algorithms.

Findings

The proposed total variation functional is highly rotation-invariant.

The new framework outperforms existing algorithms in numerical experiments.

It eliminates stagnation issues present in previous BM3D-MRI methods.

Abstract

Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration.