– F. X Dupé (LIF) : Toward a general greedy approach for sparse optimization

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Date(s) - 18 octobre 2013

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Toward a general greedy approach for sparse optimization\n\nBy François Xavier Dupé, LIF.\n\nAbstract : Following recent works on greedy sparse minimization like\nCoSaMP or GRASP, we propose a generalization (based on GRASP idea) of\nthe CoSaMP greedy method for general sparse optimization. By defining a\nRIP-like criterion for non-linear operator (e.g. gradient), we are to\nshow that, under given conditions, such method may converge to a unique\nsolution. We illustrate the proposed framework by proposing a new greedy\nmethod to denoise Poisson degraded images by using the Moreau-Yosida\nregularization of the Poisson likelihood. The regularization provides us\nwith a data fidelity term with nice properties which we minimize under\nsparsity constraints. We provide numerical experiments which show the\nsoundness of the method compared to the convex l1-norm relaxation of the\nproblem.[