An EM algorithm for convolutive independent component analysis

Abstract In this paper, we address the problem of blindly separating convolutive mixtures of spatially and temporally independent sources. Source densities are modelled as mixtures of Gaussians. We present an EM algorithm to compute Maximum Likelihood estimates of both the separating filters and the source density parameters, whereas in the state-of-the-art separating filters are usually estimated with gradient descent techniques. The use of the EM algorithm, as an alternative to the usual gradient descent techniques, is advantageous as it provides a faster and more stable convergence and as it does not require the empirical tuning of a learning rate. Besides, we show how multichannel autoregressive spectral estimation techniques can be used in order to properly initialize the EM algorithm. We demonstrate the efficiency of our EM algorithm together with the proposed initialization scheme by reporting on simulations with artificial mixtures. Finally, we discuss the theoretical and practical limitations of our EM approach and point out possible ways of addressing these issues in future works.