Minimization of a sparsity promoting criterion for the recovery of complex-valued signals

Abstract : Ill-conditioned inverse problems are often encountered in signal/image processing. In this respect, convex objective functions including a sparsity promoting penalty term can be used. However, most of the existing optimization algorithms were developed for real-valued signals. In this paper, we are interested in complex-valued data. More precisely, we consider a class of penalty functions for which the associated regularized minimization problem can be solved numerically by a forward-backward algorithm. Functions within this class can be used to promote the sparsity of the solution. An application to parallel Magnetic Resonance Imaging (pMRI) reconstruction where complex-valued images are reconstructed is considered.
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https://hal.inria.fr/inria-00369590
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Submitted on : Friday, March 20, 2009 - 2:13:50 PM
Last modification on : Thursday, March 7, 2019 - 3:34:12 PM
Long-term archiving on : Thursday, June 10, 2010 - 5:45:27 PM

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  • HAL Id : inria-00369590, version 1

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Lotfi Chaâri, Jean-Christophe Pesquet, Amel Benazza-Benyahia, Philippe Ciuciu. Minimization of a sparsity promoting criterion for the recovery of complex-valued signals. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369590⟩

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