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 little is known 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. We derive iterative methods from statistical principles, however, the resulting dynamics are nonlinear and solutions may blow up. We devise a class of discrete ordinary integral differential equations 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.