Multigrid methods for total variation

TL;DR

This paper introduces a multigrid forward-backward splitting method tailored for total variation regularized inverse imaging problems, demonstrating improved efficiency in denoising and MRI applications.

Contribution

It develops a novel multigrid approach with convergence proof for nonsmooth total variation problems, focusing on dual formulations and coarse-grid problem design.

Findings

Effective in total variation denoising

Improves MRI image reconstruction

Converges under nonsmooth coherence conditions

Abstract

Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging problems, specifically, their dual problems, for which we develop in detail the relevant coarse-grid problems. We demonstrate the performance of our method on total variation denoising and magnetic resonance imaging.