Optimum mixture estimator for single-channel speech separation

In this paper, we present proofs for optimum mixture estimator for mixture estimator for single-channel speech separation (SSCS) problem. We demonstrate that by replacing the proposed optimum estimator with mixture-maximization (Mixmax) or Quadratic estimators, it is possible to reach at a lower estimation error while separating mixture of speech signals. In addition, the proposed estimator results in less cross-talk as well as higher perceptual quality in the separated speech signals. Compared to other estimators including Mixmax, the proposed method attains these merits without using non-linear mapping used in Mixmax i.e. taking log and inverse-log. Experimental results on real speech data also confirm the superiority of the proposed estimator to others in Mean Square Error (MSE) sense.