Dereverberation in noisy environments using reference signals and a maximum likelihood estimator

In speech communication systems the received microphone signals are commonly degraded by reverberation and ambient noise that can decrease the fidelity and intelligibility of a desired speaker. Reverberation can be modeled as nonstationary diffuse sound which is not directly observable. In this work, we derive an optimal signal-dependent informed spatial filter to reduce jointly reverberation and noise. In addition, we derive a novel maximum likelihood estimator for the power spectral density (PSD) of the diffuse sound, that makes use of a set of linearly independent reference signals. Experimental results show, that the proposed method provides an accurate estimate of the diffuse PSD, even with a small number of microphones. The proposed method outperforms two existing methods and is able to provide an optimal tradeoff between noise reduction and dereverberation.