Blind Source Separation of Nonstationary Convolutive Mixtures

The problem of separating convolutive mixtures of unknown time series arises in several application domains, a prominent example being the so-called cocktail party problem, where we want to recover the speech signals of multiple speakers who are simultaneously talking in a room. The room may be very reverberant due to reflections on the walls, i.e., the original source signals of our separation problem are filtered by a multiple input and multiple output (MIMO) system before they are picked up by the sensors. In Blind Source Separation (BSS), we are interested in finding a corresponding demixing MIMO system.

It has been shown that on real-world signals with some time-structure, second-order statistics generates enough constraints to solve the BSS problem in principle, by utilizing one of the following two signal properties:

While there are several algorithms for convolutive mixtures utilizing nonstationarity, both in the time domain and in the frequency domain, there are currently very few approaches taking the nonwhiteness property into account. A third approach to blind source separation is to apply independent component analysis (ICA). Here, we utilize the Although in theory, each of these three properties is known to be sufficient, it has recently been shown that in practical scenarios, the combination of these criteria can lead to improved performance.

Our Contributions

In [C03-3] we present a rigorous derivation of a more general class of algorithms for convolutive mixtures based on second-order statistics by first introducing a general matrix formulation for convolutive mixtures following [C03-1] that includes all time lags. The approach leads to a number of new insights and utilizes both, the nonwhiteness property and the nonstationarity property and is suitable for on-line and off-line algorithms by introducing a general weighting function allowing for tracking of time-varying environments [C03-1].

For both, the time-domain and broadband frequency-domain versions, there are interesting links to well-known and extended algorithms as special cases [C03-3,C03-2]. The new broadband frequency-domain approach for BSS inherently avoids well-known problems of conventional (narrowband) frequency-domain BSS, such as the permutation of the individual frequency component, and the circularity problem. Moreover, using the so-called generalized coherence, we established links between the time-domain and traditional frequency-domain algorithms and have shown that our cost function leads to an update equation with an inherent normalization giving a very robust and fast adaptation, even in reverberant environments.

The new broadband BSS approach has recently led to powerful high-quality realtime BSS implementations on regular PC platforms (portable integrated solution on a laptop computer). So far, broadband-based BSS systems have been considered unfeasible in realtime with previous time-domain approaches.

In [C03-7][B04-1] we further generalize the approach of [C03-3] by exploiting all three above mentioned signal properties. While this derivation is based on a generalized information-theoretic criterion, [C03-3] turns out to be a special case (the optimum second-order case) of [C03-7] for Gaussian sources. In [B04-1] a complete treatment including time-domain and broadband frequency-domain algorithms is given, and new efficient approximations are outlined.

For more information contact Herbert Buchner or Robert Aichner.

Related Publications


[C04-7] H. Buchner, R. Aichner, and W. Kellermann, "TRINICON: A Versatile Framework for Multichannel Blind Signal Processing," Conf. Rec. IEEE Intl. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Montreal, Canada, May 2004. Invited Paper.

[C04-1] R. Aichner, H. Buchner, and W. Kellermann, "Convolutive Blind Source Separation for Noisy Mixtures," Proc. Joint Meeting of the German and the French Acoustical Societies (CFA/DAGA) , Strasbourg, France, March 2004.
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[B04-1] H. Buchner, R. Aichner, and W. Kellermann, "Blind Source Separation for Convolutive Mixtures: A Unified Treatment," In Y.Huang and J. Benesty (eds.), Audio Signal Processing for Next-Generation Multimedia Communication Systems, Kluwer Academic Publishers, Boston/Dordrecht/London, to appear 2004.

[C03-10] W. Kellermann and H. Buchner, "Wideband Algorithms versus Narrowband Algorithms for Adaptive Filtering in the DFT Domain," Proc. Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, November 2003. Invited Paper.

[C03-7] H. Buchner, R. Aichner, and W. Kellermann, "Blind Source Separation for Convolutive Mixtures Exploiting Nongaussianity, Nonwhiteness, and Nonstationarity," Conf. Rec. IEEE Intl. Workshop on Acoustic Echo and Noise Control (IWAENC), Kyoto, Japan, September 2003.

[C03-3] H. Buchner, R. Aichner, and W. Kellermann, "A Generalization of a Class of Blind Source Separation Algorithms for Convolutive Mixtures," Proc. IEEE Int. Symposium on Independent Component Analysis and Blind Source Separation (ICA), Nara, Japan, April 2003.

[C03-2] R. Aichner, H. Buchner, S. Araki, and S. Makino, "On-line Time-Domain Blind Source Separation of Nonstationary Convolved Signals," Proc. IEEE Int. Symposium on Independent Component Analysis and Blind Source Separation (ICA), Nara, Japan, April 2003.

[C03-1] R. Aichner, H. Buchner, and W. Kellermann, "Comparison and a Theoretical Link Between Time-Domain and Frequency-Domain Blind Source Separation," Proc. 29th Annual German Conf. on Acoustics (DAGA), Aachen, Germany, March 2003.

[B03-1] H. Buchner, J. Benesty, and W. Kellermann, "Multichannel Frequency-Domain Adaptive Filtering with Application to Acoustic Echo Cancellation," In J.Benesty and Y.Huang (eds.), Adaptive signal processing: Application to real-world problems, Springer-Verlag, Berlin/Heidelberg, Jan 2003.

Latest update: Apr, 2004