Iterative regularization via dual diagonal descent

TL;DR

This paper introduces a primal-dual diagonal descent method for linear inverse problems, providing convergence and stability guarantees, and demonstrating state-of-the-art performance through numerical experiments.

Contribution

It presents a novel iterative regularization algorithm applicable to broad regularizers and data-fit terms, with rigorous convergence and stability analysis.

Findings

Proves convergence of the proposed method.

Establishes stability under data perturbations.

Achieves state-of-the-art results in numerical tests.

Abstract

In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal {descent} method. Our analysis establishes convergence as well as stability results. Theoretical findings are complemented with numerical experiments showing state of the art performances.