Dictionary Identifiability from Few Training Samples

Rémi Gribonval (1) , Karin Schnass (2)

1 METISS - Speech and sound data modeling and processing
2 LTS2 - EPFL

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.

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

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