Shift-invariant dictionary learning for sparse representations: extending K-SVD

Boris Mailhé (1) , Sylvain Lesage (1) , Rémi Gribonval (1) , Frédéric Bimbot (1) , Pierre Vandergheynst (2, 3)

1 METISS - Speech and sound data modeling and processing
2 SP Lab - Laboratoire de Traitement du signal [EPFL] / Signal Processing Laboratories
3 LTS2 - EPFL

Shift-invariant dictionaries are generated by taking all the possible shifts of a few short patterns. They are helpful to represent long signals where the same pattern can appear several times at different positions. We present an algorithm that learns shift invariant dictionaries from long training signals. This algorithm is an extension of K-SVD. It alternates a sparse decomposition step and a dictionary update step. The update is more difficult in the shift-invariant case because of occurrences of the same pattern that overlap. We propose and evaluate an unbiased extension of the method used in K-SVD, i.e. a method able to exactly retrieve the original dictionary in a noiseless case.

Mots clés: dictionary learning; shift invariance; sparse approximation; K-SVD

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

Boris Mailhé, Sylvain Lesage, Rémi Gribonval, Frédéric Bimbot, Pierre Vandergheynst. Shift-invariant dictionary learning for sparse representations: extending K-SVD. EUropean SIgnal Processing COnference (EUSIPCO'08), Aug 2008, Lausanne, Switzerland. 5 p. ⟨hal-00350165⟩