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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(More)
We consider the problem of deconvolving an image with a priori information on its representation in a frame. Our vari-ational approach consists of minimizing the sum of a residual energy and a separable term penalizing each frame coefficient individually. This penalization term may model various properties, in particular sparsity. A general iterative method(More)
Regularization techniques have been in use in signal recovery for over four decades. In this paper, we propose a new, synthetic approach to the study of regularization methods in image denoising problems based on Moreau's proximity operators. We exploit the remarkable properties enjoyed by these operators to establish in a systematic fashion a variety of(More)
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