Probabilistic blind deconvolution of non-stationary sources

We solve a class of blind signal separation problems using a constrained linear Gaussian model. The observed signal is modelled by a convolutive mixture of colored noise signals with additive white noise. We derive a time-domain EM algorithm `KaBSS´ which estimates the source signals, the associated second-order statistics, the mixing filters and the observation noise covariance matrix. KaBSS invokes the Kalman smoother in the Estep to infer the posterior probability of the sources, and one-step lower bound optimization of the mixing filters and noise covariance in the M-step. In line with (Parra and Spence, 2000) the source signals are assumed time variant in order to constrain the solution sufficiently. Experimental results are shown for mixtures of speech signals.