Dictionary Identifiability from Few Training Samples

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $ell^1$ minimisation, or more precisely the problem of identifying a dictionary $dico$ from a set of training samples $Y$ knowing that $Y = dico X$ for some coefficient matrix $X$. It provides a characterisation of coefficient matrices $X$ that allow to recover any orthonormal basis (ONB) as a local minimum of an $ell^1$ minimisation problem. Based on this characterisation it is shown that certain types of sparse random coefficient matrices will ensure local identifiability of the ONB with high probability.


Publié dans:
Proc. EUSIPCO'08
Présenté à:
EUSIPCO, Lausanne, August 2008
Année
2008
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 Notice créée le 2008-02-25, modifiée le 2019-03-16

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