Optimization of a Geman-McClure like criterion for sparse signal deconvolution

Abstract : This paper deals with the problem of recovering a sparse unknown signal from a set of observations. The latter are obtained by convolution of the original signal and corruption with additive noise. We tackle the problem by minimizing a least-squares fit criterion penalized by a Geman-McClure like potential. The resulting criterion is a rational function, which makes it possible to formulate its minimization as a generalized problem of moments for which a hierarchy of semidefinite programming relaxations can be proposed. These convex relaxations yield a monotone sequence of values which converges to the global optimum. To overcome the computational limitations due to the large number of involved variables, a stochastic block-coordinate descent method is proposed. The algorithm has been implemented and shows promising results
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CAMSAP 2015 : 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Dec 2015, Cancun, Mexico. IEEE, Proceedings CAMSAP 2015 : 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp.317-320, 2015, 〈10.1109/CAMSAP.2015.7383798 〉
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Marc Castella, Jean-Christophe Pesquet. Optimization of a Geman-McClure like criterion for sparse signal deconvolution. CAMSAP 2015 : 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Dec 2015, Cancun, Mexico. IEEE, Proceedings CAMSAP 2015 : 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp.317-320, 2015, 〈10.1109/CAMSAP.2015.7383798 〉. 〈hal-01263352v2〉

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