Multichannel Dereverberation Theorems and Robustness Issues

Multichannel dereverberation amounts to the inversion of a multiple-input/multiple-output linear time-invariant system. In this paper, necessary and sufficient conditions for perfect dereverberation using stable and finite impulse response (FIR) filters are established. It is then shown that the inverse system given by the pseudoinverse of the original transfer function matrix exhibits a noise reduction property. A necessary and sufficient condition under which this pseudoinverse system is FIR is also given. Further, an FIR approximation to the pseudoinverse system is considered and the effects of the length of this approximation on the dereverberation accuracy are investigated. Finally, an analytical and numerical assessment of the dependence of the dereverberation accuracy on the accuracy of the acquisition of room impulse responses is provided.