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Conference Papers Year : 2008

Dictionary Identifiability from Few Training Samples

Karin Schnass
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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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inria-00544764 , version 1 (06-02-2011)


  • HAL Id : inria-00544764 , version 1


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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