A Bayesian approach to spatial filtering and diffuse power estimation for joint dereverberation and noise reduction

A spatial filter, with L linear constraints that are based on instantaneous narrowband direction-of-arrival (DOA) estimates, was recently proposed to obtain a desired spatial response for at most L sound sources. In noisy and reverberant environments, it becomes difficult to get reliable instantaneous DOA estimates and hence obtain the desired spatial response. In this work, we develop a Bayesian approach to spatial filtering that is more robust to DOA estimation errors. The resulting filter is a weighted sum of spatial filters pointed at a discrete set of DOAs, with the relative contribution of each filter determined by the posterior distribution of the discrete DOAs given the microphone signals. In addition, the proposed spatial filter is able to reduce both reverberation and noise. In this work, the required diffuse sound power is estimated using the posterior distribution of the discrete set of DOAs. Simulation results demonstrate the ability of the proposed filter to achieve strong suppression of the undesired signal components with small amount of signal distortion, in noisy and reverberant conditions.