Hicham Saylani

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.

Blind separation of convolutive mixtures of non-stationary sources using joint block diagonalization in the frequency domain

We recently proposed a new method based on spectral decorrelation for blindly separating linear instantaneous mixtures of nonstationary sources. In this paper, we propose a generalization of this method to FIR convolutive mixtures using a second-order approach based on block-diagonalization of covariance matrices in the frequency domain. Contrary to similar time or time-frequency domain methods, our approach requires neither the piecewise stationarity of the sources nor their sparseness. The simulation results show the better performance of our approach compared to these methods.

Blind separation of convolutive mixtures of non-stationary and temporally uncorrelated sources based on joint diagonalization

In this paper, we propose a new method for blindly separating convolutive mixtures of non-stationary and temporally uncorrelated sources. It estimates each source and its delayed versions up to a scale factor by Jointly Diagonalizing a set of covariance matrices in the frequency domain, contrary to most existing second-order methods which require a Block Joint Diagonalization algorithm followed by a blind deconvolution to achieve the same result. Consequently, our method is much faster than these classical methods especially for higer-order mixing filters and may lead to better performance as confirmed by our simulation results.