Frequency-domain single-channel inverse filtering for speech dereverberation: Theory and practice

The objective of single-channel inverse filtering is to design an inverse filter that achieves dereverberation while being robust to an inaccurate room impulse response (RIR) measurement or estimate. Since a stable and causal inverse filter typically does not exist, approximate time-domain inverse filtering techniques such as singlechannel least-squares (SCLS) have been proposed. However, besides being computationally expensive and often infeasible, SCLS generally leads to distortions in the output signal in the presence of RIR inaccuracies. In this paper, a theoretical analysis is initially provided, showing that the direct inversion of the acoustic transfer function in the frequency-domain generally yields instability and acausality issues. In order to resolve these issues, a novel frequency-domain inverse filtering technique is proposed that incorporates regularization and uses a single-channel speech enhancement scheme. Experimental results demonstrate that the proposed technique yields a higher dereverberation performance and has a significantly lower computational complexity compared to the SCLS technique.