Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Preprint -learning unions of orthonormal bases with thresholded singular value decomposition

Sylvain Lesage 1 Rémi Gribonval 1 Frédéric Bimbot 1 Laurent Benaroya 1
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : We propose a new method to learn overcomplete dictionaries for sparse coding. The method is designed to learn dictionaries structured as unions of orthonormal bases. The interest of such a structure is manifold. Indeed, it seems that many signals or images can be modeled as the super-imposition of several layers with sparse decompositions in as many bases. Moreover, in such dictionaries, the efficient Block Coordinate Relaxation (BCR) algorithm can be used to compute sparse decompositions. We show that it is possible to design an iterative learning algorithm that produces a dictionary with the required structure. Each step is based on the coefficients estimation, using a variant of BCR, followed by the update of one chosen basis, using Singular Value Decomposition. We assess experimentally how well the learning algorithm recovers dictionaries that may or may not have the required structure, and to what extent the noise level is a disturbing factor.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [11 references]  Display  Hide  Download
Contributor : Rémi Gribonval Connect in order to contact the contributor
Submitted on : Saturday, November 18, 2017 - 8:54:38 AM
Last modification on : Tuesday, June 15, 2021 - 4:27:26 PM
Long-term archiving on: : Monday, February 19, 2018 - 12:31:10 PM


Files produced by the author(s)


  • HAL Id : hal-01637825, version 1


Sylvain Lesage, Rémi Gribonval, Frédéric Bimbot, Laurent Benaroya. Preprint -learning unions of orthonormal bases with thresholded singular value decomposition. 2004. ⟨hal-01637825⟩



Record views


Files downloads