A Majorize-Minimize memory gradient method for complex-valued inverse problems

Anisia Florescu 1 Emilie Chouzenoux 2 Jean-Christophe Pesquet 2 Philippe Ciuciu 3 Silviu Ciochina 1
1 University Politehnica of Bucharest [Bucarest, Roumanie]
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 LNAO - Laboratoire de Neuroimagerie Assistée par Ordinateur
Abstract : Complex-valued data are encountered in many application areas of signal and image processing. In the context of optimization of functions of real variables, subspace algorithms have recently attracted much interest, owing to their efficiency for solving large-size problems while simultaneously offering theoretical convergence guarantees. The goal of this paper is to show how some of these methods can be successfully extended to the complex case. More precisely, we investigate the properties of the proposed complex-valued Majorize-Minimize Memory Gradient (3MG) algorithm. Important practical applications of these results arise in inverse problems. Here, we focus on image reconstruction in Parallel Magnetic Resonance Imaging (PMRI). The linear operator involved in the observation model then includes a subsampling operator over the $k$-space (spatial Fourier domain) the choice of which is analyzed through our numerical results. In addition, sensitivity matrices associated with the multiple coil channels come into play. Comparisons with existing optimization methods confirm the good performance of the proposed algorithm.
Keywords : complex-valued signals optimization subspace algorithms descent methods majorization-minimization image reconstruction inverse problems magnetic resonance imaging sampling proximal methods
Type de document :
Article dans une revue
Signal Processing, Elsevier, 2014, 103, pp.285-295. <10.1016/j.sigpro.2013.09.026>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00829788
Contributeur : Emilie Chouzenoux <>
Soumis le : lundi 3 juin 2013 - 17:25:03
Dernière modification le : vendredi 11 septembre 2015 - 09:57:14
Document(s) archivé(s) le : mercredi 4 septembre 2013 - 04:14:46

Fichier

complex3MG_hal.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

CEA | LIGM | ENPC-LIGM | PARISTECH | LIGM_SIGNAL | UNIV-MLV | UPEC-UPEM | ENPC | LABEX-BEZOUT

Citation

Anisia Florescu, Emilie Chouzenoux, Jean-Christophe Pesquet, Philippe Ciuciu, Silviu Ciochina. A Majorize-Minimize memory gradient method for complex-valued inverse problems. Signal Processing, Elsevier, 2014, 103, pp.285-295. <10.1016/j.sigpro.2013.09.026>. <hal-00829788>

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de
la notice

487

Téléchargements du document

369

Contact

support.ccsd.cnrs.fr
hal.support@ccsd.cnrs.fr
Logo CCSD