The analysis of the simplification from the ideal ratio to binary mask in signal-to-noise ratio sense

• We theoretically investigate the SNR gain of the ideal binary mask (IBM) and the ideal ratio mask (IRM).
• We find that the approximate W-Disjoint Orthogonality (AWDO) assumption almost holds due to the sparse nature of speech.
• Under AWDO assumption, we derive an upper bound of the difference between the two ideal masks.
• We derive the optimal linear mask model which achieves higher SNR gain than the IRM.

For speech separation systems, the ideal binary mask (IBM) can be viewed as a simplified goal of the ideal ratio mask (IRM) which is derived from Wiener filter. The available research usually verify the rationality of this simplification from the aspect of speech intelligibility. However, the difference between the two masks has not been addressed rigorously in the signal-to-noise ratio (SNR) sense. In this paper, we analytically investigate the difference between the two ideal masks under the assumption of the approximate W-Disjoint Orthogonality (AWDO) which almost holds under many kinds of interference due to the sparse nature of speech. From the analysis, one theoretical upper bound of the difference is obtained under the AWDO assumption. Some other interesting discoveries include a new ratio mask which achieves higher SNR gains than the IRM and the essential relation between the AWDO degree and the SNR gain of the IRM.