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Proximal Splitting Methods in Signal Processing

In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author

Listed:
  • Patrick L. Combettes

    (UPMC Université Paris 06)

  • Jean-Christophe Pesquet

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.

Suggested Citation

  • Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9569-8_10
    DOI: 10.1007/978-1-4419-9569-8_10
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