Multi-microphone speech dereverberation using eigen-decomposition

A family of approaches for multi-microphone speech dereverberation in colored noise environments, using eigen-decomposition of the data correlation matrix, is explored in this chapter. It is shown that the Acoustic Impulse Responses (AIRs), relating the speech source and the microphones are embedded in the null subspace of the received signals. The null subspace is estimated using either the generalized singular value decomposition of the data matrix or the generalized eigen-value decomposition of the respective correlation matrix. In cases where the channel order is overestimated, further processing is required. A closed-form algorithm for extracting the AIR is derived. The proposed algorithm exploits the special structure of the null subspace matrix by using the total least squares criterion. A study of the incorporation of the subspace method into a subband framework has potential to improve the performance of the proposed method, although many problems, especially the gain ambiguity problem, remain open. The estimated AIRs can be used for dereverberation by applying conventional channel inversion methods. An experimental study supports the potential of the proposed method, and provides insight into its limitations.