Stochastic approximation and a nonlocally weighted soft-constrained recursive algorithm for blind separation of reverberant speech mixtures

We review statistical equations for blind source separation problems, then introduce their stochastic approximation and recursive algorithms. The recurrence resembles discretization of nonlinear systems of ordinary differential equations which may not have global solutions in general. Though scaling variables were used before to control finite time blowup, instabilities may arise from small divisor problem during silent periods of speech signals, and asymptotic balance as a necessary condition for convergence was ignored. To resolve these deficiencies, we propose a nonlocally weighted soft-constrained recursive algorithm. The nonlocal weighting of the iterations promotes stability and convergence of the algorithm. The scaling variables evolve by soft-constrained difference equations. Computations on synthetic speech mixtures based on measured binaural room impulse responses in enclosed rooms with reverberation time up to 1 second show that the new algorithm achieves consistently higher signal-to-interference ratio improvement than existing methods. The algorithm is observed to be stable and convergent, and is applied to separation of room recorded mixtures of song and music as well.