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SIGNAL RECOVERY BY PROXIMAL FORWARD-BACKWARD SPLITTING
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| Venue: | MULTISCALE MODEL. SIMUL. TO APPEAR |
| Citations: | 509 - 24 self |
BibTeX
@MISC{Combettes_signalrecovery,
author = {Patrick L. Combettes and Valérie R. Wajs},
title = {SIGNAL RECOVERY BY PROXIMAL FORWARD-BACKWARD SPLITTING },
year = {}
}
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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.
Keyphrases
signal recovery proximal forward-backward splitting multiscale model generic problem stability result convex function disparate problem monotone operator simplified analysis texture image decomposition scheme signal recovery certain regularity property large class forward-backward algorithm iterative method derive existence proximity operator various inverse problem recent result standardized fashion
