Iterative image deconvolution using overcomplete representations

Abstract : We consider the problem of deconvolving an image with a priori information on its representation in a frame. Our variational approach consists of minimizing the sum of a residual energy and a separable term penalizing each frame coef - cient individually. This penalization term may model various properties, in particular sparsity. A general iterative method is proposed and its convergence is established. The novelty of this work is to extend existing methods on two distinct fronts. First, a broad class of convex functions are allowed in the penalization term which, in turn, yields a new class of soft thresholding schemes. Second, while existing results are restricted to orthonormal bases, our algorithmic framework is applicable to much more general overcomplete representations. Numerical simulations are provided.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00621888
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  • HAL Id : hal-00621888, version 1

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Caroline Chaux, Patrick Louis Combettes, Jean-Christophe Pesquet, Valérie R. Wajs. Iterative image deconvolution using overcomplete representations. European Signal Processing Conference (EUSIPCO'06), Sep 2006, Florence, Italy. 10pp. ⟨hal-00621888⟩

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