  This article describes a probabilistic formulation of a Weighted Power
minimization Distortionless response convolutional beamformer (WPD). The WPD
unifies a weighted prediction error based dereverberation method (WPE) and a
minimum power distortionless response beamformer (MPDR) into a single
convolutional beamformer, and achieves simultaneous dereverberation and
denoising in an optimal way. However, the optimization criterion is obtained
simply by combining existing criteria without any clear theoretical
justification. This article presents a generative model and a probabilistic
formulation of a WPD, and derives an optimization algorithm based on a maximum
likelihood estimation. We also describe a method for estimating the steering
vector of the desired signal by utilizing WPE within the WPD framework to
provide an effective and efficient beamformer for denoising and
dereverberation.
