A nonlocally weighted soft-constrained natural gradient iterative method is introduced for robust blind separation in reverberant environment. The nonlocal weighting of the iterations promotes stability and convergence of the algorithm for long demixing filters. The scaling degree of freedom is controlled by soft-constraints built into the auxiliary difference equations. The small divisor problem of iterations in silence durations of speech is resolved. Computations on synthetic speech mixtures based on measured binaural room impulse responses show that the algorithm achieves higher signal-to-inteference ratio improvement than existing method (natural gradient time domain algorithm) in an office size room with reverberation time over 0.5 second.

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A convex speech enhancement (CSE) method is presented based on convex optimization and pause detection of the speech sources. Channel spatial difference is identified for enhancing each speech source individually while suppressing other interfering sources. Sparse unmixing filters indicating channel spatial differences are sought by <i>l</i> ₁ norm regularization and the split Bregman method. A subdivided split Bregman method is developed for efficiently solving the problem in severely reverberant environments. The speech pause detection is based on a binary mask source separation method. The CSE method is evaluated objectively and subjectively, and found to outperform a list of existing blind speech separation approaches on both synthetic and room recorded speech mixtures in terms of the overall computational speed and separation quality.