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Journal Articles Inverse Problems Year : 2008

A proximal decomposition method for solving convex variational inverse problems

Abstract

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of nonsmooth functions and establish its weak convergence. The algorithm fully decomposes the problem in that it involves each function individually via its own proximity operator. A significant improvement over the methods currently in use in the area of inverse problems is that it is not limited to two nonsmooth functions. Numerical applications to signal and image processing problems are demonstrated.

Dates and versions

hal-00692901 , version 1 (01-05-2012)

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Patrick Louis Combettes, Jean-Christophe Pesquet. A proximal decomposition method for solving convex variational inverse problems. Inverse Problems, 2008, 24 (6), ⟨10.1088/0266-5611/24/6/065014⟩. ⟨hal-00692901⟩
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