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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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https://hal.inria.fr/inria-00544764
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Submitted on : Sunday, February 6, 2011 - 11:07:00 PM
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  • HAL Id : inria-00544764, version 1

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Rémi Gribonval, Karin Schnass. Dictionary Identifiability from Few Training Samples. European Signal Processing Conference (EUSIPCO'08), Aug 2008, Lausanne, Switzerland. ⟨inria-00544764⟩

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