A global optimization approach for rational sparsity promoting criteria

Abstract : We consider the problem of recovering an unknown signal observed through a nonlinear model and corrupted with additive noise. More precisely, the nonlinear degradation consists of a convolution followed by a nonlinear rational transform. As a prior information, the original signal is assumed to be sparse. We tackle the problem by minimizing a least-squares fit criterion penalized by a Geman-McClure like potential. In order to find a globally optimal solution to this rational minimization problem, we transform it in a generalized moment problem, for which a hierarchy of semidefinite programming relaxations can be used. To overcome computational limitations on the number of involved variables, the structure of the problem is carefully addressed, yielding a sparse relaxation able to deal with up to several hundreds of optimized variables. Our experiments show the good performance of the proposed approach
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EURASIP. EUSIPCO 2017 - 25th European Signal Processing Conference, Aug 2017, Kos Island, Greece. IEEE, 2017 25th European Signal Processing Conference (EUSIPCO), pp.156 - 160, 2017, 〈10.23919/EUSIPCO.2017.8081188〉
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Marc Castella, Jean-Christophe Pesquet. A global optimization approach for rational sparsity promoting criteria. EURASIP. EUSIPCO 2017 - 25th European Signal Processing Conference, Aug 2017, Kos Island, Greece. IEEE, 2017 25th European Signal Processing Conference (EUSIPCO), pp.156 - 160, 2017, 〈10.23919/EUSIPCO.2017.8081188〉. 〈hal-01666536〉

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