Proximal Splitting Methods in Signal Processing

Patrick L. Combettes () and Jean-Christophe Pesquet
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Patrick L. Combettes: UPMC Université Paris 06

Chapter Chapter 10 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 185-212 from Springer

Abstract: 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 inverse problems and, especially, in 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.

Keywords: Alternating-direction method of multipliers; Backward–backward algorithm; Convex optimization; Denoising; Douglas–Rachford algorithm; Forward–backward algorithm; Frame; Landweber method; Iterative thresholding; Parallel computing; Peaceman–Rachford algorithm; Proximal algorithm; Restoration and reconstruction; Sparsity; Splitting (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-9569-8_10

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