Blind speech separation employing directional statistics in an Expectation Maximization framework

In this paper we propose to employ directional statistics in a complex vector space to approach the problem of blind speech separation in the presence of spatially correlated noise. We interpret the values of the short time Fourier transform of the microphone signals to be draws from a mixture of complex Watson distributions, a probabilistic model which naturally accounts for spatial aliasing. The parameters of the density are related to the a priori source probabilities, the power of the sources and the transfer function ratios from sources to sensors. Estimation formulas are derived for these parameters by employing the Expectation Maximization (EM) algorithm. The E-step corresponds to the estimation of the source presence probabilities for each time-frequency bin, while the M-step leads to a maximum signal-to-noise ratio (MaxSNR) beamformer in the presence of uncertainty about the source activity. Experimental results are reported for an implementation in a generalized sidelobe canceller (GSC) like spatial beamforming configuration for 3 speech sources with significant coherent noise in reverberant environments, demonstrating the usefulness of the novel modeling framework.