Accelerated iterative regularization via dual diagonal descent

TL;DR

This paper introduces an accelerated dual diagonal descent algorithm for linear inverse problems, achieving optimal convergence rates and stability with various regularization and data-fit functions, including complex divergences.

Contribution

It develops an inertial accelerated iterative method with convergence and stability analysis for a broad class of inverse problems and data-fit functions.

Findings

Proves convergence and stability of the proposed algorithm.

Achieves optimal convergence rates for additive data-fit terms.

Extends analysis to complex divergences like Kullback-Leibler.

Abstract

We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we analyze both convergence and stability. Using tools from inexact proximal calculus, we prove early stopping results with optimal convergence rates for additive data-fit terms as well as more general cases, such as the Kullback-Leibler divergence, for which different type of proximal point approximations hold.