# Maximum likelihood convolutional beamformer for simultaneous denoising and dereverberation

## TL;DR

This paper introduces a probabilistic maximum likelihood approach to a convolutional beamformer that simultaneously denoises and dereverberates speech signals, unifying existing methods with a solid theoretical foundation.

## Contribution

It presents a generative probabilistic model for the WPD beamformer and derives an optimization algorithm based on maximum likelihood estimation, enhancing theoretical justification.

## Key findings

- Effective simultaneous denoising and dereverberation achieved.
- Probabilistic formulation improves theoretical understanding.
- Steering vector estimation enhances beamformer performance.

## Abstract

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.