Solving monotone inclusions involving parallel sums of linearly composed maximally monotone operators

TL;DR

This paper introduces two primal-dual algorithms for solving complex structured monotone inclusions involving parallel sums of maximally monotone operators, with applications in imaging and total variation models.

Contribution

It presents novel primal-dual splitting methods specifically designed for parallel sums of linearly composed maximally monotone operators, enhancing solution techniques for structured monotone problems.

Findings

Developed two primal-dual algorithms for structured monotone inclusions.

Algorithms effectively handle parallel sums of maximally monotone operators.

Applications demonstrated in imaging problems with total variation functionals.

Abstract

The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some elaborated splitting techniques, all of the operators occurring in the problem formulation are processed individually via forward or backward steps. The treatment of parallel sums of linearly composed maximally monotone operators is motivated by applications in imaging which involve first- and second-order total variation functionals, to which a special attention is given.