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

Lotfi Chaâri; Jean-Christophe Pesquet; Amel Benazza-Benyahia; Philippe Jean-Pierre ; Pierre Ciuciu

inria-00369590, version 1

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

Lotfi Chaâri () ^1, 2, Jean-Christophe Pesquet () ¹, Amel Benazza-Benyahia () ³, Philippe Jean-Pierre ; Pierre Ciuciu () ²

SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations (2009)

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.

1: Laboratoire d'Informatique Gaspard-Monge (LIGM)
Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049
2: Service NEUROSPIN (NEUROSPIN)
CEA : DSV/I2BM
3: unité de Recherche en Imagerie Satellitaire et ses Applications (URISA)
Univerité Tunis Carthage 7 novembre

inria-00369590, version 1
http://hal.inria.fr/inria-00369590
oai:hal.inria.fr:inria-00369590
From: Ist Rennes <>
Submitted on: Friday, 20 March 2009 14:13:50
Updated on: Friday, 20 March 2009 14:14:36

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