Penalty function based joint diagonalization approach for convolutive constrained BSS of nonstationary signals

In this paper, we address convolutive blind source separation (BSS) of speech signals in the frequency domain and explicitly exploit the second order statistics (SOS) of nonstationary signals. Based on certain constraints on the BSS solution, we propose to reformulate the problem as an unconstrained optimization problem by using nonlinear programming techniques. The proposed algorithm therefore utilizes penalty functions with the cross-power spectrum based criterion and thereby converts the task into a joint diagonalization problem with unconstrained optimization. Using this approach, not only can the degenerate solution induced by a null unmixing matrix and the over-learning effect existing at low frequency bins be automatically removed, but a unifying view to joint diagonalization with unitary or nonunitary constraint is provided. Numerical experiments verify the validity of the proposed approach.