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

Date(s) : 18/10/2013   iCal
14 h 00 min - 15 h 00 min

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.

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