A Riemannian approach to blind separation of t-distributed sources

The blind source separation problem is considered through the approach based on non-stationarity and coloration. In both cases, the sources are usually assumed to be Gaussian. In this paper, we extend previous works in order to handle sources drawn from the multivariate Student t-distribution. After studying the structure of the parameter manifold in this case, a new blind source separation criterion based on the log-likelihood of the considered distribution is proposed. To solve the resulting optimization problem, Riemannian optimization on the parameter manifold is leveraged. Practical expressions of the mathematical tools required by first order based Riemmanian optimization methods for this parameter manifold are derived to this end. The performance of the proposed method is illustrated on simulated data.