An Algorithm for Splitting Parallel Sums of Linearly Composed Monotone Operators, with Applications to Signal Recovery

TL;DR

This paper introduces a novel primal-dual splitting algorithm for complex structured monotone inclusions, with applications to image and signal recovery, and demonstrates its effectiveness through numerical simulations.

Contribution

It develops a new algorithm that handles sums, linear compositions, and parallel sums of monotone operators, advancing methods for structured monotone inclusion problems.

Findings

Algorithm converges asymptotically in Hilbert spaces.

Effective in solving structured monotone inclusion problems.

Numerical results confirm practical applicability in signal recovery.

Abstract

We present a new primal-dual splitting algorithm for structured monotone inclusions in Hilbert spaces and analyze its asymptotic behavior. A novelty of our framework, which is motivated by image recovery applications, is to consider inclusions that combine a variety of monotonicity-preserving operations such as sums, linear compositions, parallel sums, and a new notion of parallel composition. The special case of minimization problems is studied in detail, and applications to signal recovery are discussed. Numerical simulations are provided to illustrate the implementation of the algorithm.