L. Condat (GIPSA-lab) : A new primal-dual splitting algorithm for convex optimization\; application as a heuristic for super-resolution

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Date(s) - 30/01/2015
14 h 00 min - 15 h 00 min

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Summary: A new splitting algorithm is proposed to minimize the sum of\nconvex functions\, potentially nonsmooth and composed with linear\noperators. This generic formulation encompasses numerous regularized\ninverse problems in image processing. The algorithm\, whose weak\nconvergence is proved\, calls the individual gradient or proximity\noperators of the functions\, without any inner loop or linear system to\nsolve. The classical Douglas-Rachford\, forward-backward and\nChambolle-Pock algorithms are recovered as particular cases. In the\nsecond part of the talk (joint work with A. Hirabayashi\, Kyoto\, Japan)\,\nI address the problem of recovering a spike train from noisy lowpass\nmeasurements\, through a reformulation as a structured low rank matrix\napproximation problem. Used as a heuristic for this nonconvex problem\,\nthe proposed algorithm yields state-of-the-art results.

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