Multigrid methods for total variation

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.

Deanonymised version of the article submitted (and later accepted) to Scale-Space and Variational Methods (SSVM) 2025. This version does not incorporate post peer review improvements