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Signal Recovery by Proximal Forward-Backward Splitting

Combettes, Patrick L., Wajs, Valérie R.·2005·Multiscale Modeling & Simulation
DOI 10.1137/050626090
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Abstract

We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis for a variety of existing iterative methods. Applications to geometry/texture image decomposition schemes are also discussed. A novelty of our framework is to use extensively the notion of a proximity operator, which was introduced by Moreau in the 1960s.

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Metadata

Authors
Combettes, P. L., & Wajs, V. R.
Venue
Multiscale Modeling & Simulation
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2005-01
Volume
4
Issue
4
Pages
1168-1200
ISSN
  • 1540-3459 (ISSN-L)
  • 1540-3467
DOI
10.1137/050626090
OpenAlex
W2006262045
Cited by
2,678
References
0
FWCI
24.47
Type
journal article
Language
en
Open access
closed

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Combettes, P. L., & Wajs, V. R. (2005). Signal Recovery by Proximal Forward-Backward Splitting. Multiscale Modeling & Simulation. https://doi.org/10.1137/050626090

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