Underdetermined Blind Separation using Multi-Subspace Representation in Time-Frequency Domain

Blind source separation (BSS) is a technique to recognize the multiple talkers from the multiple observations received by some sensors without any prior knowledge information. The problem is that the mixing is always complex, i.e., nonlinear, underdetermined mixture, such as the case where sources are mixed with some direction angles, or where the number of sensors is less than that of sources. In this paper, we propose a multi-subspace representation based BSS approach that allows the mixing process to be nonlinear and underdetermined. The approach relies on a multi-layer representation and sparse representation in time-frequency (TF) domain. By parameterizing such subspaces, we can map the observed signals in the feature space with the coefficient matrix from the parameter space. We then exploit the linear mixture in the feature space that corresponds to the nonlinear mixture in the input space. Once such subspaces are built, the coefficient matrix can be constructed by solving an l₁-regularization on the coding coefficient vector. Relying on the TF representation, the target matrix can be constructed in a sparse mixture TF vectors with a fewer computational cost. The experiments are run on the observations that are generated from nonlinear functions, and that are collected with some direction angles in a virtual room environment. The proposed approach exhibits a higher separation accuracy than that of the conventional algorithms.