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.

Patrick L. Combettes

Valérie R. Wajs

Multiscale Modeling and Simulation

Multiscale Model. Simul.

Signal Recovery by Proximal Forward-Backward Splitting

It is shown 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, which 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.

Category	Quartile
数学	4
数学, 数学跨学科应用	3
数学, 物理数学物理	3

Signal Recovery by Proximal Forward-Backward Splitting

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	2