Multi-channel PSD Estimators for Speech Dereverberation: a Theoretical and Experimental Comparison

In this paper we perform an extensive theoretical and experimental comparison of two recently proposed multi-channel speech dereverberation algorithms. Both of them are based on the multi-channel Wiener filter but they use different estimators of the speech and reverberation power spectral densities (PSDs). We first derive closed-form expressions for the mean square error (MSE) of both PSD estimators and then show that one estimator – previously used for speech dereverberation by the authors – always yields a better MSE. Only in the case of a two microphone array or for special spatial distributions of the interference both estimators yield the same MSE. The theoretically derived MSE values are in good agreement with numerical simulation results and with instrumental speech quality measures in a realistic speech dereverberation task for binaural hearing aids.