Maximum likelihood estimation of the late reverberant power spectral density in noisy environments

An estimate of the power spectral density (PSD) of the late reverberation is often required by dereverberation algorithms. In this work, we derive a novel multichannel maximum likelihood (ML) estimator for the PSD of the reverberation that can be applied in noisy environments. The direct path is first blocked by a blocking matrix and the output is considered as the observed data. Then, the ML criterion for estimating the reverberation PSD is stated. As a closed-form solution for the maximum likelihood estimator (MLE) is unavailable, a Newton method for maximizing the ML criterion is derived. Experimental results show that the proposed estimator provides an accurate estimate of the PSD, and is outperforming competing estimators. Moreover, when used in a multi-microphone noise reduction and dereverberation algorithm, the estimated reverberation PSD is shown to provide improved performance measures as compared with the competing estimators.