Under-determined speech separation using GMM-based non-linear beamforming

This paper introduces a frequency-domain non-linear beamformer that can perform speech source separation of under-determined mixtures, is reasonably artifact-free and does not require prior knowledge of the number of speakers. This beamformer utilises a Gaussian mixture distribution to model the observation probability density in each frequency bin, which can be learnt using the expectation maximisation (EM) algorithm. A linear minimum-variance distortionless response (MVDR) beamformer is determined for each of the Gaussian components. The proposed non-linear beamformer is then a weighted sum of these linear MVDR beamformers and is therefore also distortionless. The relative contribution for each linear MVDR beamformer is calculated as the posterior probability (specific to each time-frequency point) of its corresponding Gaussian component. Simulation results of the non-linear beamformer in under-determined mixtures with room reverberation confirm its ability to successfully separate speech sources with virtually no artifacts.