BLIND SEPARATION OF SOURCES WITH SPARSE REPRESENTATIONS IN A GIVEN SIGNAL DICTIONARY

Michael Zibulevsky Barak A. Pearlmutter
michael@cs.unm.edu bap@cs.unm.edu

The blind source separation problem is to extract the underlying source signals from a set of linear mix- tures, where the mixing matrix is unknown. We con- sider a two-stage separation process. First, a pri- ori selection of a possibly overcomplete signal dictio- nary (e.g. wavelet frame, learned dictionary, etc.) in which the sources are assumed to be sparsely repre- sentable. Second, unmixing the sources by exploiting the their sparse representability. We consider the gen- eral case of more sources than mixtures, but also de- rive a more e∆cient algorithm in the case of a non- overcomplete dictionary and equal numbers of sources and mixtures. Experiments with arti cial signals and with musical sounds demonstrate signi cantly better separation than other known techniques.