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Blind source separation for time-variant mixing systems using piecewise linear approximations

In this paper we address the problem of blind source separation when the mixing system is time-variant. We address the problem using piecewise linearly variant unmixing matrices in time as an approximation. Using optimization theory we are able to transform the independent component analysis problem to handle linearly time-variant unmixing matrices. Using a time-adaptive whitening pre-processing step, ICA in the lie-group domain, and an optimization problem in the original unmixing matrix domain we are able to get accurate results for synthetically generated signals, bringing significant improvements over time-invariant ICA methods.