Proximal Splitting Methods in Signal Processing

Understand

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.