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      A Proximal Decomposition Method for Solving Convex Variational Inverse Problems

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          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 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.

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          Most cited references 30

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          An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

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            Splitting Algorithms for the Sum of Two Nonlinear Operators

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              On Projection Algorithms for Solving Convex Feasibility Problems

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                Author and article information

                Journal
                2008-07-16
                2009-06-23
                Article
                10.1088/0266-5611/24/6/065014
                0807.2617

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.OC math.NA

                Numerical & Computational mathematics, Numerical methods

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