Joint estimation of late reverberant and speech power spectral densities in noisy environments using Frobenius norm

Various dereverberation and noise reduction algorithms require power spectral density estimates of the anechoic speech, reverberation, and noise. In this work, we derive a novel multichannel estimator for the power spectral densities (PSDs) of the reverberation and the speech suitable also for noisy environments. The speech and reverberation PSDs are estimated from all the entries of the received signals power spectral density (PSD) matrix. The Frobenius norm of a general error matrix is minimized to find the best fitting PSDs. Experimental results show that the proposed estimator provides accurate estimates of the PSDs, and is outperforming competing estimators. Moreover, when used in a multi-microphone noise reduction and dereverberation algorithm, the estimated reverberation and speech PSDs are shown to provide improved performance measures as compared with the competing estimators.