Separation of Periodically Time-Varying Mixtures Using Second-Order Statistics

We address the problem of Blind Source Separation (BSS) in the context of instantaneous (memoryless) linear mixtures, where the unknown mixing coefficients are time varying, changing periodically in time. Such a mixing model is realistic, e.g., when considering a biological or physiological system where the mixing coefficients are affected by periodic processes like breathing, heart-beating etc. Assuming stationary sources with distinct spectra, we rely on second-order statistics (SOS) and offer an expansion of the classical Second Order Blind Identification (SOBI) algorithm, accommodating the periodic variation model. The proposed algorithm consists of estimating several types of correlation matrices related to the time-varying SOS of the observations, followed by applying generalized joint diagonalization, which leads to estimates of the parameters of the periodic mixing. These estimated parameters are used in turn to apply a time-varying unmixing operation, recovering the desired sources. In its basic form (as presented in here), the algorithm requires prior knowledge (or a good estimate) of the cyclic period. We demonstrate the performance improvement over SOBI in simulation.