Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed ${\ell _1}/{\ell _2}$
| Autor: | Jean-Christophe Pesquet, Laurent Duval, Emilie Chouzenoux, Audrey Repetti, Mai Quyen Pham |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | IEEE Signal Processing Letters. 22:539-543 |
| ISSN: | 1558-2361 1070-9908 |
| DOI: | 10.1109/lsp.2014.2362861 |
| Popis: | The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution. |
| Databáze: | OpenAIRE |
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