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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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Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Monday, February 15, 2016 - 5:28:38 PM
Last modification on : Thursday, February 4, 2021 - 3:28:26 AM
Long-term archiving on: : Saturday, November 12, 2016 - 9:30:17 PM


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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. pp.317-320, ⟨10.1109/CAMSAP.2015.7383798⟩. ⟨hal-01263352v2⟩



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