Proximal Splitting Methods in Signal Processing

Patrick Louis Combettes 1 Jean-Christophe Pesquet 2
1 LJLL - Laboratoire Jacques-Louis Lions
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
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.
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Submitted on : Tuesday, November 22, 2011 - 6:45:37 PM
Last modification on : Wednesday, May 15, 2019 - 3:47:45 AM

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Patrick Louis Combettes, Jean-Christophe Pesquet. Proximal Splitting Methods in Signal Processing. Bauschke, H.H.; Burachik, R.S.; Combettes, P.L.; Elser, V.; Luke, D.R.; Wolkowicz, H. (Eds.). Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer, pp.185-212, 2011, 978-1-4419-9568-1. ⟨10.1007/978-1-4419-9569-8⟩. ⟨hal-00643807⟩

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