I've seen a lot of methods solving noise reduction problem with wiener filter in single channel case. Since there's only one channel, we get a real value for each T-F unit by calculating the PSD of the signal. While in multi channel case, we get a complex-valued PSD matrix. How do we define the a priori SNR or other variables?
Some researchers use the trace of the matrix which involves the inverse of the noise PSD matrix, but there may be a computional problem since the noise matrix is likely to a large condition number.
A multi-channel noise reduction technique is presented based on a Speech Distortion-Weighted Multi-channel Wiener Filter (SDW-MWF) approach that incorporates the conditional Speech Presence Probability (SPP). A traditional SDW-MWF uses a fixed parameter to a trade-off between noise reduction and speech distortion without taking speech presence into account. Consequently, the improvement in noise reduction comes at the cost of a higher speech distortion since the speech dominant segments and the noise dominant segments are weighted equally. Incorporating the conditional SPP in SDW-MWF allows to exploit the fact that speech may not be present at all frequencies and at all times, while the noise can indeed be continuously present. In speech dominant segments it is then desirable to have less noise reduction to avoid speech distortion, while in noise dominant segments it is desirable to have as much noise reduction as possible. Experimental results with hearing aid scenarios demonstrate that the proposed SDW-MWF incorporating the conditional SPP improves the signal-to-noise ratio compared to a traditional SDW-MWF.
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