Regularization for Partial Multichannel Equalization for Speech Dereverberation

Abstract

Acoustic multichannel equalization techniques such as the multiple-input/output inverse theorem (MINT), which aim to equalize the room impulse responses (RIRs) between the source and the microphone array, are known to be highly sensitive to RIR estimation errors. To increase robustness, it has been proposed to incorporate regularization in order to decrease the energy of the equalization filters. In addition, more robust partial multichannel equalization techniques such as relaxed multichannel least-squares (RMCLS) and channel shortening (CS) have recently been proposed. In this paper, we propose a partial multichannel equalization technique based on MINT (P-MINT) which aims to shorten the RIR. Furthermore, we investigate the effectiveness of incorporating regularization to further increase the robustness of P-MINT and the aforementioned partial multichannel equalization techniques, i.e., RMCLS and CS. In addition, we introduce an automatic non-intrusive procedure for determining the regularization parameter based on the L-curve. Simulation results using measured RIRs show that incorporating regularization in P-MINT yields a significant performance improvement in the presence of RIR estimation errors, whereas a smaller performance improvement is observed when incorporating regularization in RMCLS and CS. Furthermore, it is shown that the intrusively regularized P-MINT technique outperforms all other investigated intrusively regularized multichannel equalization techniques in terms of perceptual speech quality (PESQ). Finally, it is shown that the automatic non-intrusive regularization parameter in regularized P-MINT leads to a very similar performance as the intrusively determined optimal regularization parameter, making regularized P-MINT a robust, perceptually advantageous, and practically applicable multichannel equalization technique for speech dereverberation.