Underdetermined blind source separation by latent component estimation

Abstract

In this dissertation, the problem of blindly separating sources of various statistical distributions from the underdetermined mixtures is considered. The sources are assumed to be composed of two orthogonal components: one lies in the rowspace and the other in the nullspace of a mixing matrix. The mapping from the rowspace component to the mixtures by the mixing matrix is invertible usingthe pseudo-inverse of the mixing matrix. The mapping from the nullspace component to zero by the mixing matrix is non-invertible, and there are infinitely many solutions to the nullspace component. That is, the nullspace component is latent. This dissertation proposes the nullspace component estimator that leads to a source estimator that is optimal in the MSE sense. In order to characterize and model a wide variety of source distribution required in the estimation, the parametric generalized Gaussian distribution is used, and its parameters are estimated based on the expectation-maximization algorithm. When the mixing matrix is unavailable, it must be estimated, and a novel algorithm based on a single source detection algorithm, which detects time-frequency regions of single source occupancy, is proposed. In our simulations, the proposed algorithm, compared to other conventional algorithms, estimated the mixing matrix with higher accuracy and separated various sources with higher signal-to-interference ratio.