Parallel proximal methods for total variation minimization

TL;DR

This paper introduces a parallel proximal-gradient algorithm for total variation minimization that simplifies computation and guarantees convergence, improving efficiency for large-scale imaging inverse problems.

Contribution

It proposes a novel parallel proximal method that replaces the standard proximal step with independent proximals, enabling efficient large-scale TV minimization.

Findings

Converges to the TV solution without sub-iterations

Simplifies the proximal step for TV minimization

Enhances applicability to large-scale imaging problems

Abstract

Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our method replaces the standard proximal step of TV by a simpler alternative that computes several independent proximals. We prove that the proposed parallel proximal method converges to the TV solution, while requiring no sub-iterations. The results in this paper could enhance the applicability of TV for solving very large scale imaging inverse problems.