Time domain blind source separation of non-stationary convolved signals by utilizing geometric beamforming

We propose a time-domain BSS algorithm that utilizes geometric information such as sensor positions and assumed locations of sources. The algorithm tackles the problem of convolved mixtures by explicitly exploiting the non-stationarity of the acoustic sources. The learning rule is based on secondorder statistics and is derived by natural gradient minimization. The proposed initialization of the algorithm is based on the null beamforming principle. This method leads to improved separation performance, and the algorithm is able to estimate long unmixing FIR filters in the time domain due to the geometric initialization. We also propose a post-filtering method for dewhitening which is based on the scaling technique in frequency-domain BSS. The validity of the proposed method is shown by computer simulations. Our experimental results confirm that the algorithm is capable of separating real-world speech mixtures and can be applied to short learning data sets down to a few seconds. Our results also confirm that the proposed dewhitening post-filtering method maintains the spectral content of the original speech in the separated output. INTRODUCTION Blind source separation (BSS) refers to the problem of recovering signals from several observed linear mixtures. The adjective “blind” stresses the fact that the source signals are not observed and that no information on the mixing process is available. The lack of a priori knowledge of the mixing system is compensated by a statistically strong but physically plausible assumption of independence. The weakness of the prior information is precisely the strength of the BSS model. Thus BSS has received considerable attention in the last few years, and many algorithms have been proposed [4, 5, 6, 10]. However, the separation of broadband signals in reverberant environments remains a challenging problem. This work was performed while the author was with the University of Applied Sciences Regensburg. Currently the author is at the Telecommunications Laboratory, University of Erlangen-Nuremberg. In this paper we consider the BSS of convolutive mixtures of speech. Many researchers have proposed frequency domain algorithms, which in general transform the convolutive mixture problem in the time domain to multiple instantaneous mixtures in the frequency domain. However, in [3] it was shown that for long reverberation the separation performance of frequency domain BSS degrades for long FFT frame sizes. This was our motivation in approaching the convolutive BSS problem in the time domain. CONVOLUTIVE BSS MODEL In real environments, where sound travels slowly compared to the distances in a typical acoustic environment, the signal arrives at the sensors with different time delays. This scenario is referred to as a multi-path environment and can be described as a finite impulse response (FIR) convolutive mixture: