BLIND SEPARATION OF MORE SOURCES THAN MIXTURES USING SPARSITY OF THEIR SHORTTIME FOURIER TRANSFORM
Pau Bofill \Lambda, Michael Zibulevsky y
pau@ac.upc.es, michael@cs.unm.edu
This paper focuses on underdetermined Blind Source
Separation, that is, the separation of N sources from
M linear mixtures when M ! N . We exploit the spar
sity of the shorttime Fourier transform when applied
to music and speech signals. Given the mixing ma
trix, a sparse representation of the sources is obtained
by solving a lowdimensional linear programming (LP)
problem for each of the data points independently. For
M = 2 we propose a shortest path, closedform solution
to this LP problem that represents each data point as
a linear combination of the pair of directions that en
close it. The mixing matrix can be estimated either by
maximizing a likelihood function, using the above LP
optimization at the internal step, or with a clustering
algorithm that gives a much faster solution. In this
work, for M = 2 we use a clustering algorithm based
on a triangular potential function which infers both the
mixing matrix and the number of sources.
Several experiments involving music and speech
signals are described, including the separation of six
sources from two mixtures.