Adaptive Signal Processing pp 195-225 | Cite as

# Blind Source Separation of Convolutive Mixtures of Speech

## Abstract

This chapter introduces the blind source separation (BSS) of convolutive mixtures of acoustic signals, especially speech. A statistical and computational technique, called independent component analysis (ICA), is examined. By achieving nonlinear decorrelation, nonstationary decorrelation, or time-delayed decorrelation, we can find source signals only from observed mixed signals. Particular attention is paid to the physical interpretation of BSS from the acoustical signal processing point of view. Frequency-domain BSS is shown to be equivalent to two sets of frequency domain adaptive microphone arrays, i.e., adaptive beamformers (ABFs). Although BSS can reduce reverberant sounds to some extent in the same way as ABF, it mainly removes the sounds from the jammer direction. This is why BSS has difficulties with long reverberation in the real world. If sources are not “independent,” the dependence results in bias noise when obtaining the correct unmixing filter coefficients. Therefore, the performance of BSS is limited by that of ABF. Although BSS is upper bounded by ABF, BSS has a strong advantage over ABF. BSS can be regarded as an intelligent version of ABF in the sense that it can adapt without any information on the array manifold or the target direction, and sources can be simultaneously active in BSS.

## Keywords

Independent Component Analysis Speech Signal Independent Component Analysis Blind Source Separation Blind Separation## Preview

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## References

- 1.J. F. Cardoso, “The three easy routes to independent component analysis; contrasts and geometry,” in
*Proc. Conference Indep. Compon. Anal. Signal. Sep.*, Dec. 2001, pp. 1–6.Google Scholar - 2.T. W. Lee, A. J. Bell, and R. Orglmeister, “Blind source separation of real world signals,”
*Neural Networks*, vol. 4, pp. 2129–2134, 1997.Google Scholar - 3.M. Z. Ikram and D. R. Morgan, “Exploring permutation inconsistency in blind separation of speech signals in a reverberant environment,” in
*Proc. ICASSP*, June 2000, pp. 1041–1044.Google Scholar - 4.S. Araki, S. Makino, T. Nishikawa, and H. Saruwatari, “Fundamental limitation of frequency domain blind source separation for convolutive mixture of speech,” in
*Proc. ICASSP*, May 2001, vol. 5, pp. 2737–2740.Google Scholar - 5.S. Araki, S. Makino, R. Mukai, and H. Saruwatari, “Equivalence between frequency domain blind source separation and frequency domain adaptive null beamformers,” in
*Proc. Eurospeech*, Sept. 2001, pp. 2595–2598.Google Scholar - 6.R. Mukai, S. Araki, and S. Makino, “Separation and dereverberation performance of frequency domain blind source separation for speech in a reverberant environment,” in
*Proc. Eurospeech*, Sept. 2001, pp. 2599–2602.Google Scholar - 7.S. C. Douglas, “Blind separation of acoustic signals,” in
*Microphone Arrays: Techniques and Applications*, M. Brandstein and D. B. Ward, Eds., pp. 355– 380, Springer, Berlin, 2001.Google Scholar - 8.K. Torkkola, “Blind separation of delayed and convolved sources,” in
*Unsupervised Adaptive Filtering*,*Vol. I*, S. Haykin, Ed., pp. 321–375, John Wiley & Sons, 2000.Google Scholar - 9.E. Weinstein, M. Feder, and A. V. Oppenheim, “Multi-channel signal separation by decorrelation,”
*IEEE Trans. Speech Audio Processing*, vol. 1, no. 4, pp. 405– 413, Oct. 1993.Google Scholar - 10.T. W. Lee,
*Independent Component Analysis -Theory and Applications*, Kluwer, 1998.Google Scholar - 11.M. Kawamoto, A. K. Barros, A. Mansour, K. Matsuoka, and N. Ohnishi, “Real world blind separation of convolved non-stationary signals,” in
*Proc. Workshop Indep. Compon. Anal. Signal. Sep.*, Jan. 1999, pp. 347–352.Google Scholar - 12.X. Sun and S. Douglas, “A natural gradient convolutive blind source separation algorithm for speech mixtures,” in
*Proc. Conference Indep. Compon. Anal. Signal. Sep.*, Dec. 2001, pp. 59–64.Google Scholar - 13.P. Smaragdis, “Blind separation of convolved mixtures in the frequency domain,”
*Neurocomputing*, vol. 22, pp. 21–34, 1998.MATHCrossRefGoogle Scholar - 14.S. Ikeda and N. Murata, “A method of ICA in time-frequency domain,” in
*Proc. Workshop Indep. Compon. Anal. Signal. Sep.*, Jan. 1999, pp. 365–370.Google Scholar - 15.R. Aichner, S. Araki, S. Makino, T. Nishikawa, and H. Saruwatari, “Time domain blind source separation of non-stationary convolved signals by utilizing geometric beamforming,” in
*Proc. NNSP*, Sept. 2002.Google Scholar - 16.J. Anemüeller and B. Kollmeier, “Amplitude modulation decorrelation for convolutive blind source separation,” in
*Proc. Workshop Indep. Compon. Anal. Signal. Sep.*, 2000, pp. 215–220.Google Scholar - 17.F. Asano, S. Ikeda, M. Ogawa, H. Asoh, and N. Kitawaki, “A combined approach of array processing and independent component analysis for blind separation of acoustic signals,” in
*Proc. ICASSP*, May 2001, vol. 5, pp. 2729–2732.Google Scholar - 18.J. Herault and C. Jutten, “Space or time adaptive signal processing by neural network models,” in
*Neural Networks for Computing: AIP Conference Proceedings**151*, J. S. Denker, Ed., American Institute of Physics, New York, 1986.Google Scholar - 19.C. Jutten and J. Herault, “Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture,”
*Signal Processing*, vol. 24, pp. 1–10, 1991.MATHCrossRefGoogle Scholar - 20.P. Comon, C. Jutten, and J. Herault, “Blind separation of sources, part II: problems statement,”
*Signal Processing*, vol. 24, pp. 11–20, 1991.MATHCrossRefGoogle Scholar - 21.E. Sorouchyari, “Blind separation of sources, part III: stability analysis,”
*Signal Processing*, vol. 24, pp. 21–29, 1991.MATHCrossRefGoogle Scholar - 22.A. Cichocki and L. Moszczynski, “A new learning algorithm for blind separation of sources,”
*Electronics Letters*, vol. 28, no. 21, pp. 1986–1987, 1992.CrossRefGoogle Scholar - 23.J. F. Cardoso and A. Souloumiac, “Blind beamforming for non-gaussian signals,”
*IEE Proceedings-F*, vol. 140, no. 6, pp. 362–370, Dec. 1993.Google Scholar - 24.P. Comon, “Independent component analysis–a new concept?,”
*Signal Processing*, vol. 36, no. 3, pp. 287–314, Apr. 1994.MATHCrossRefGoogle Scholar - 25.A. Cichocki and R. Unbehauen, “Robust neural networks with on-line learning for blind identification and blind separation of sources,”
*IEEE Trans. Circuits and Systems*, vol. 43, no. 11, pp. 894–906, 1996.CrossRefGoogle Scholar - 26.T. W. Lee, M. Girolami, A. J. Bell, and T. J. Sejnowski, “A unifying information-theoretic framework for independent component analysis,”
*Computers and Mathematics with Applications*, vol. 31, no. 11, pp. 1–12, Mar. 2000.MathSciNetCrossRefGoogle Scholar - 27.A. Hyvärinen, H. Karhunen, and E. Oja,
*Independent Component Analysis*, John Wiley & Sons, 2001.Google Scholar - 28.S. Haykin,
*Unsupervised Adaptive Filtering*, John Wiley & Sons, 2000.Google Scholar - 29.A. Cichocki and S. Amari,
*Adaptive Blind Signal and Image Processing*, John Wiley & Sons, 2002.Google Scholar - 30.A. J. Bell and T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,”
*Neural Computation*, vol. 7, no. 6, pp. 1129–1159, 1995.CrossRefGoogle Scholar - 31.S. Amari, A. Cichocki, and H. Yang, “A new learning algorithm for blind source separation,” in
*Advances in Neural Information Processing Systems**8*, pp. 757– 763, MIT Press, 1996.Google Scholar - 32.K. Matsuoka, M. Ohya, and M. Kawamoto, “A neural net for blind separation of nonstationary signals,”
*Neural Networks*, vol. 8, no. 3, pp. 411–419, 1995.CrossRefGoogle Scholar - 33.L. Molgedey and H. G. Schuster, “Separation of a mixure of independent signals using time delayed correlations,”
*Physical Review Letters*, vol. 72, no. 23, pp. 3634–3636, 1994.CrossRefGoogle Scholar - 34.A. Belouchrani, K. A. Meraim, J. F. Cardoso, and E. Moulines, “A blind source separation technique based on second order statistics,”
*IEEE Trans. Signal Processing*, vol. 45, no. 2, pp. 434–444, Feb. 1997.CrossRefGoogle Scholar - 35.L. Parra and C. Spence, “Convolutive blind separation of non-stationary sources,”
*IEEE Trans. Speech Audio Processing*, vol. 8, no. 3, pp. 320–327, May 2000.CrossRefGoogle Scholar - 36.S. Amari, “Natural gradient works efficiently in learning,”
*Neural Computation*, vol. 10, pp. 251–276, 1998.CrossRefGoogle Scholar - 37.H. Sawada, R. Mukai, S. Araki, and S. Makino, “Polar coordinate based nonlinear function for frequency-domain blind source separation,” in
*Proc. ICASSP*, May 2002, vol. 1, pp. 1001–1004.Google Scholar - 38.S. Kurita, H. Saruwatari, S. Kajita, K. Takeda, and F. Itakura, “Evaluation of blind signal separation method using directivity pattern under reverberant conditions,” in
*Proc. ICASSP*, June 2000, pp. 3140–3143.Google Scholar - 39.L. Parra and C. Alvino, “Geometric source separation: Merging convolutive source separation with geometric beamforming,” in
*Proc. NNSP*, Sept. 2001, pp. 273–282.Google Scholar - 40.S. Araki, S. Makino, R. Mukai, Y. Hinamoto, T. Nishikawa, and H. Saruwatari, “Equivalence between frequency domain blind source separation and frequency domain adaptive beamforming,” in
*Proc. ICASSP*, May 2002, vol. 2, pp. 1785– 1788.Google Scholar - 41.M. Knaak and D. Filbert, “Acoustical semi-blind source separation for machine monitoring,” in
*Proc. Conference Indep. Compon. Anal. Signal. Sep.*, Dec. 2001, pp. 361–366.Google Scholar - 42.H. Saruwatari, S. Kurita, and K. Takeda, “Blind source separation combining frequency-domain ICA and beamforming,” in
*Proc. ICASSP*, May 2001, pp. 2733–2736.Google Scholar - 43.O. L. Frost, “An algorithm for linearly constrained adaptive array processing,” in
*Proc. IEEE*, Aug. 1972, vol. 60, pp. 926–935.CrossRefGoogle Scholar - 44.S. Araki, S. Makino, R. Mukai, T. Nishikawa, and H. Saruwatari, “Fundamental limitation of frequency domain blind source separation for convolved mixture of speech,” in
*Proc. Conference Indep. Compon. Anal. Signal. Sep.*, Dec. 2001, pp. 132–137.Google Scholar - 45.S. Gerven and D. Compernolle, “Signal separation by symmetric adaptive decorrelation: stability, convergence, and uniqueness,”
*IEEE Trans. Signal Processing*, vol. 43, no. 7, pp. 1602–1612, July 1995.CrossRefGoogle Scholar - 46.R. Mukai, S. Araki, and S. Makino, “Separation and dereverberation performance of frequency domain blind source separation,” in
*Proc. Conference Indep. Compon. Anal. Signal. Sep.*, Dec. 2001, pp. 230–235.Google Scholar