Proximal Splitting Methods in Signal Processing

TL;DR

This paper reviews the properties of proximity operators and introduces proximal splitting methods, unifying various algorithms for convex optimization in signal processing applications such as signal recovery and synthesis.

Contribution

It provides a comprehensive overview of proximal splitting methods and demonstrates their application in signal processing, extending existing algorithms within a unified framework.

Findings

Proximal splitting methods unify several convex optimization algorithms.

These methods are effective in signal recovery and synthesis tasks.

The paper highlights the importance of proximity operators in signal processing.

Abstract

The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems, has recently been introduced in the arena of signal processing, where it has become increasingly important. In this paper, we review the basic properties of proximity operators which are relevant to signal processing and present optimization methods based on these operators. These proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. Applications of proximal methods in signal recovery and synthesis are discussed.