OMP AND CONTINUOUS DICTIONARIES: IS k-STEP RECOVERY POSSIBLE?

Clément Elvira 1 Rémi Gribonval 1 Charles Soussen 2 Cedric 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 : In this work, 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 build up a family of dictionaries for which k-step recovery is possible with OMP for 1-dimensional parameters. In higher dimension, algebraic conditions become necessary and will lead us to revisit some well-known k-step discrete analyses. Finally, a toy-example illustrates the level of tightness of our sufficient conditions.
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Submitted on : Wednesday, March 6, 2019 - 1:42:50 PM
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Clément Elvira, Rémi Gribonval, Charles Soussen, Cedric Herzet. OMP AND CONTINUOUS DICTIONARIES: IS k-STEP RECOVERY POSSIBLE?. ICASSP 2019 - IEEE 44th International Conference on Acoustics, Speech, and Signal Processing, IEEE, May 2019, Brighton, United Kingdom. ⟨10.1109/ICASSP.2019.8683617⟩. ⟨hal-02049486v2⟩

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