Blind separation of linear instantaneous mixtures of non-stationary signals in the frequency domain

Blind source separation (BSS) methods aim at restoring source signals from their mixtures. For linear instantaneous mixtures of stationary random sources, a natural and widely used approach consists in using some statistics associated to the temporal representation of the signals. On the contrary, we here consider non-stationary real sources and we show that they have interesting frequency-domain properties which motivate the introduction of two new frequency-domain BSS methods. The first method works by diagonalizing a zero-lag, second-order statistics matrix, created using both covariance and pseudo-covariance matrices of Fourier transforms of real-valued observations. In practice, this method is specially suitable for separating cyclo-stationary sources. The second method is particularly important because it allows the existing time-domain algorithms developed for stationary, temporally correlated sources (like AMUSE or SOBI) to be extended to non-stationary, temporally uncorrelated sources just by mapping the mixtures into the frequency domain. Both methods set no constraint on the piecewise stationarity of the sources, unlike most previously reported BSS methods exploiting source non-stationarity. The experimental results using artificial and real-world sources confirm the good performance of the proposed methods for non-stationary sources.