The Coherence Function in Blind Source Separation of Convolutive Mixtures of Non-stationary Signals

We propose a new performance criteria and update mechanism for the blind decorrelation of an array of sensor measurements into independent sources, assuming each sensor measures a different convolutive mixture of statistically independent non-stationary sources. Specifically, the criteria is the sum of the magnitude squared coherence functions between all possible distinct pairs of outputs produced by a matrix of adaptable filters operating on the sensor measurements in the frequency domain. We then derive an efficient overlap-save online update equation based on stochastic gradient descent and recursive estimation of the coherence functions. We demonstrate separation within fractions of a second and convergence within a few seconds on real room recordings. We attribute this speed to the normalization and recursive estimates of the coherence functions.