Best Basis Compressed Sensing

Gabriel Peyré (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

This paper proposes an extension of compressed sensing that allows to express the sparsity prior in a dictionary of bases. This enables the use of the random sampling strategy of compressed sensing together with an adaptive recovery process that adapts the basis to the structure of the sensed signal. A fast greedy scheme is used during reconstruction to estimate the best basis using an iterative refinement. Numerical experiments on sounds and geometrical images show that adaptivity is indeed crucial to capture the structures of complex natural signals.

Mots clés: Compressed sensing; adaptivity; best basis; inverse problem

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Gabriel Peyré. Best Basis Compressed Sensing. Scale Space and Variational Methods in Computer Vision (SSVM'07), Jun 2007, Ischia, Italy. pp.80-91, ⟨10.1007/978-3-540-72823-8_8⟩. ⟨hal-00365607⟩