Soft-Constrained Iterative Methods for
Blind Source Separation

Jack Xin ((UC Irvine)

Abstract:

Blind source separation is a
statistical inverse problem aiming to recover source signals and mixing
filters (discrete Green's functions) without detailed knowledge of the
environment. Cocktail party problem is an example of how humans perform
this task by paying attention. Yet much remains to be
discovered of the computation inside human brain for this task.
For sound mixtures, source signals viewed as time series are much more
independent of each other than their mixtures. The separation is
formulated mathematically as minimization of generalized cross
correlations. Iterative methods are derived from statistical
principles, however, the resulting dynamics are nonlinear and solutions
may blow up. A class of discrete integral differential equations
are introduced to impose soft constraints, and control the scaling
behavior of iterations. The solutions then exist globally and
converge in some weak sense to the desired separation
conditions. Performance on synthetic mixtures and room
recording of sounds will be demonstrated.