Underdetermined Blind Separation of Audio Sources from the Time-Frequency Representation of their Convolutive Mixtures

This paper considers the blind separation of nonstationary sources in the underdetermined convolutive mixture case. We introduce two methods based on the sparsity assumption of the sources in the time-frequency (TF) domain. The first one assumes that the sources are disjoint in the TF domain; i.e. there is at most one source signal present at a given point in the TF domain. In the second method, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present (active) at a TF point should be strictly less than the number of sensors. In that case, the separation can be achieved thanks to subspace projection which allows us to identify the active sources and to estimate their corresponding time-frequency distribution (TFD) values.