Dictionary identifiability from few training samples (2008)
| Venue: | in Proc. EUSIPCO’08 |
| Citations: | 5 - 2 self |
BibTeX
@INPROCEEDINGS{Gribonval08dictionaryidentifiability,
author = {Rémi Gribonval and Projet Metiss and Centre De Recherche Inria and Karin Schnass},
title = {Dictionary identifiability from few training samples},
booktitle = {in Proc. EUSIPCO’08},
year = {2008}
}
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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 Φ from a set of training samples Y knowing that Y = ΦX 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. 1.
