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A broad range of inverse problems can be abstracted into the problem ofminimizing the sum of several convex functions in a Hilbert space. We propose aproximal decomposition algorithm for solving this problem with an arbitrarynumber of nonsmooth functions and establish its convergence. The algorithmfully decomposes the problem in that it involves each function individually viaits own proximity operator. A significant improvement over the methodscurrently in use in the area of inverse problems is that it is not limited totwo nonsmooth functions. Numerical applications to signal and image processingproblems are demonstrated.

A Proximal Decomposition Method for Solving Convex Variational Inverse Problems