A distortion free learning algorithm for multi-channel convolutive blind source separation

In this paper, source separation and signal distortion are theoretically analyzed in multi-channel convolutive blind source separation (BSS) systems implemented in both the time and the frequency domains. Feedforward (FF-) BSS systems have some degrees of freedom in the solution space. Therefore, signal distortion is likely to occur. A condition for complete separation and distortion free is proposed for multi-channel convolutive FF-BSS systems. This condition is incorporated in learning algorithms as a distortion free constraint. The condition for weights in a separation block cannot be expressed in an explicit form. Therefore, an approximation expression is introduced. Computer simulations using speech signals and stationary colored signals have been carried out for conventional methods and the new learning algorithms. The proposed method can drastically suppress signal distortion, while maintaining a high source separation performance.