Gribonval, Remi
Schnass, Karin
Dictionary Identifiability from Few Training Samples
Proc. EUSIPCO'08
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.
lts2;
sparse representation;
dictionary learning;
basis learning;
recovery condition;
random coefficients;
2008
http://infoscience.epfl.ch/record/117531/files/eusipco08.pdf;