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Séminaire du département Images et Signal du 21/03/2013 à 15h00


Alternating Direction Optimization for Convex Inverse Problems

Intervenant : Jose Manuel Bioucas Dias, Instituto de Telecomunicacoes, Lisboa, Portugal

Lieu : DIS - Salle Chartreuse (D 1121 -50 places)


Résumé : In this talk I will address  a new class of fast  of algorithms for solving  convex inverse problems where the objective function is a sum of convex terms with possibly convex constraints. Usually, one of terms in the objective function measures the data fidelity while the others, jointly with the constraints, enforce some type of regularization on the solution.
Several particular features of these problems (e.g., huge dimensionality and nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this talk, I will present a new class of algorithms to handle convex inverse problems tailored to image recovery applications. The proposed class of algorithms is an instance of the so-called alternating direction method of multipliers (ADMM), for which convergence sufficient conditions are known. We show that these conditions are satisfied by the  proposed class of algorithms.
The effectiveness of the proposed approach is illustrated in a series of imaging inverse problems, including deconvolution, reconstruction from compressive observations, and sparse  hyperspectral unmixing.

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