000134108 001__ 134108
000134108 005__ 20190416055731.0
000134108 037__ $$aCONF
000134108 245__ $$aBasis Identification from Random Sparse Samples
000134108 260__ $$c2009$$aSaint-Malo
000134108 269__ $$a2009
000134108 336__ $$aConference Papers
000134108 520__ $$aThis article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$ minimisation. The problem is to identify a dictionary $\dico$ from a set of training samples $\Y$ knowing that $\Y = \dico \X$ for some coefficient matrix $\X$. Using a characterisation of coefficient matrices $\X$ that allow to recover any basis as a local minimum of an $\ell_1$ minimisation problem, it is shown that certain types of sparse random coefficient matrices will ensure local identifiability of the basis with high probability. The necessary number of training samples grows up to a logarithmic factor linearly with the signal dimension.
000134108 6531_ $$abasis identification
000134108 6531_ $$a$\ell_1$ minimisation
000134108 6531_ $$asparse samples
000134108 6531_ $$aLTS2
000134108 6531_ $$alts2
000134108 700__ $$aGribonval, Remi
000134108 700__ $$g168927$$aSchnass, Karin$$0240457
000134108 7112_ $$dApril 6-9, 2009$$cSaint-Malo$$aSPARS09
000134108 773__ $$tProc. SPARS09
000134108 8564_ $$uhttp://spars09.inria.fr/ENGLISH/ENGLISH%20INDEX/welcome1.html$$zURL
000134108 8564_ $$uhttps://infoscience.epfl.ch/record/134108/files/spars09-56.pdf$$zn/a$$s144423
000134108 909C0 $$xU10380$$0252392$$pLTS2
000134108 909CO $$ooai:infoscience.tind.io:134108$$qGLOBAL_SET$$pconf$$pSTI
000134108 937__ $$aEPFL-CONF-134108
000134108 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000134108 980__ $$aCONF