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 eÆcient 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.