Dictionary Identifiability from Few Training Samples

Rémi Gribonval 1 Karin Schnass 2
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via L1 minimisation. The problem is to identify a dictionary Phi from a set of training samples Y knowing that Y = Phi.X for some coefficient matrix X. Using a characterisation of coefficient matrices X that allow to recover any orthonormal basis (ONB) as a local minimum of an L1 minimisation problem, it is shown that certain types of sparse random coefficient matrices will ensure local identifiability of the ONB with high probability, for a number of training samples which essentially grows linearly with the signal dimension.
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Communication dans un congrès
European Signal Processing Conference (EUSIPCO'08), Aug 2008, Lausanne, Switzerland. 2008, Proc. 16th European Signal Proccessing Conference (EUSIPCO'08). 〈http://www.eurasip.org/Proceedings/Eusipco/Eusipco2008/papers/1569104712.pdf〉
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Dernière modification le : mercredi 16 mai 2018 - 11:23:03
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Rémi Gribonval, Karin Schnass. Dictionary Identifiability from Few Training Samples. European Signal Processing Conference (EUSIPCO'08), Aug 2008, Lausanne, Switzerland. 2008, Proc. 16th European Signal Proccessing Conference (EUSIPCO'08). 〈http://www.eurasip.org/Proceedings/Eusipco/Eusipco2008/papers/1569104712.pdf〉. 〈inria-00544764〉

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