# Compressed MRI Reconstruction Exploiting a Rotation-Invariant Total Variation Discretization

arXiv: https://arxiv.org/abs/1911.11854 · HTML: https://mlsanity.com/paper/1911.11854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2019.

## Built on by (most cited first, 2 of 2)

- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [SOE: SO(3)-Equivariant 3D MRI Encoding](https://mlsanity.com/paper/2410.12053/) (2024)

## Abstract (arXiv)

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.