Abstract
Under consideration is the large body of signal recovery problems that can be formulated as the problem of minimizing the sum of two (not necessarily smooth) proper lower semicontinuous convex functions in a real Hilbert space. This generic problem is analyzed and a decomposition method is proposed to solve it. The convergence of the method, which is based on an extension of the Douglas-Rachford algorithm for monotone operators splitting, is established under general conditions. Various signal recovery applications are discussed and numerical results are provided.
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