Identification de supports en k étapes avec OMP pour les dictionnaires continus

Clément Elvira 1 Rémi Gribonval 1 Charles Soussen 2 Cédric Herzet 3
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
3 SIMSMART - SIMulation pARTiculaire de Modèles Stochastiques
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We present new theoretical results on sparse recovery guarantees for a greedy algorithm, orthogonal matching pursuit (OMP), in the context of continuous parametric dictionaries, i.e., made up of an infinite uncountable number of atoms. We characterize a family of dictionaries which definition relies on completely monotone functions (CMF), for which k-step recovery is possible with OMP for 1-dimensional parameters. In higher dimension, algebraic conditions become necessary and lead us to revisit some well-known k-step discrete analyses.
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Clément Elvira, Rémi Gribonval, Charles Soussen, Cédric Herzet. Identification de supports en k étapes avec OMP pour les dictionnaires continus. GRETSI 2019 - XXVIIème Colloque francophone de traitement du signal et des images, Aug 2019, Lille, France. pp.1-4. ⟨hal-02157571⟩

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