Learning redundant dictionaries with translation invariance property: the MoTIF algorithm

Philippe Jost 1 Pierre Vandergheynst 1 Sylvain Lesage 2 Rémi Gribonval 3
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
3 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : Sparse approximation using redundant dictionaries is an efficient tool for many applications in the field of signal processing. The performances largely depend on the adaptation of the dictionary to the signal to decompose. As the statistical dependencies are most of the time not obvious in natural high- dimensional data, learning fundamental patterns is an alternative to analytical design of bases and has become a field of acute research. Most of the time, the underlying patterns of a class of signals can be found at any time, and in the design of a dictionary, this translation invariance property should be present. We present a new algorithm for learning short generating functions, each of them building a set of atoms corresponding to all its translations. The resulting dictionary is highly redundant and translation invariant.
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Communication dans un congrès
R. Gribonval, L. Daudet, B. Torresani. SPARS'05 - Workshop on Signal Processing with Adaptive Sparse Structured Representations, 2005, Rennes, France. pp.1-3, 2005, 〈http://spars05.irisa.fr/ACTES/TS1-2.pdf〉
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Philippe Jost, Pierre Vandergheynst, Sylvain Lesage, Rémi Gribonval. Learning redundant dictionaries with translation invariance property: the MoTIF algorithm. R. Gribonval, L. Daudet, B. Torresani. SPARS'05 - Workshop on Signal Processing with Adaptive Sparse Structured Representations, 2005, Rennes, France. pp.1-3, 2005, 〈http://spars05.irisa.fr/ACTES/TS1-2.pdf〉. 〈hal-00816804〉

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