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MAP-Based Underdetermined Blind Source Separation of Convolutive Mixtures by Hierarchical Clustering and -Norm Minimization

  • Stefan Winter1, 2Email author,
  • Walter Kellermann2,
  • Hiroshi Sawada1 and
  • Shoji Makino1
EURASIP Journal on Advances in Signal Processing20062007:024717

https://doi.org/10.1155/2007/24717

Received: 30 September 2005

Accepted: 11 June 2006

Published: 5 September 2006

Abstract

We address the problem of underdetermined BSS. While most previous approaches are designed for instantaneous mixtures, we propose a time-frequency-domain algorithm for convolutive mixtures. We adopt a two-step method based on a general maximum a posteriori (MAP) approach. In the first step, we estimate the mixing matrix based on hierarchical clustering, assuming that the source signals are sufficiently sparse. The algorithm works directly on the complex-valued data in the time-frequency domain and shows better convergence than algorithms based on self-organizing maps. The assumption of Laplacian priors for the source signals in the second step leads to an algorithm for estimating the source signals. It involves the -norm minimization of complex numbers because of the use of the time-frequency-domain approach. We compare a combinatorial approach initially designed for real numbers with a second-order cone programming (SOCP) approach designed for complex numbers. We found that although the former approach is not theoretically justified for complex numbers, its results are comparable to, or even better than, the SOCP solution. The advantage is a lower computational cost for problems with low input/output dimensions.

Keywords

Hierarchical ClusterComplex NumberQuantum InformationSource SignalGood Convergence

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Authors’ Affiliations

(1)
NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Soraku-Gun, Kyoto, Japan
(2)
Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, Erlangen, Germany

References

  1. Winter S, Sawada H, Makino S: Geometrical interpretation of the PCA subspace approach for overdetermined blind source separation. EURASIP Journal on Applied Signal Processing 2006, 2006: 11 pages. special issue: Advances in Multimicrophone Speech ProcessingGoogle Scholar
  2. Matsuoka K: Independent component analysis and its applications to sound signal separation. Proceedings of the 8th International Workshop on Acoustic Echo and Noise Control (IWAENC '03), September 2003, Kyoto, Japan 15-18.Google Scholar
  3. Sawada H, Mukai R, Araki S, Makino S: A robust and precise method for solving the permutation problem of frequency-domain blind source separation. IEEE Transactions on Speech and Audio Processing 2004,12(5):530-538. 10.1109/TSA.2004.832994View ArticleGoogle Scholar
  4. Araki S, Makino S, Blin A, Mukai R, Sawada H: Underdetermined blind separation for speech in real environments with sparseness and ICA. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 3: 881-884.Google Scholar
  5. Blin A, Araki S, Makino S: Underdetermined blind separation of convolutive mixtures of speech using time-frequency mask and mixing matrix estimation. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2005,E88-A(7):1693-1700. 10.1093/ietfec/e88-a.7.1693View ArticleGoogle Scholar
  6. Bofill P, Zibulevsky M: Blind separation of more sources than mixtures using sparsity of their short-time Fourier transform. Proceedings of International Workshop on Independent Component Analysis and Blind Signal Separation (ICA '00), June 2000, Helsinki, Finland 87-92.Google Scholar
  7. Rickard S, Yilmaz Ö: On the approximate W-disjoint orthogonality of speech. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '02), May 2002, Orlando, Fla, USA 1: 529-532.Google Scholar
  8. Theis FJ: Mathematics in independent component analysis, Ph.D. thesis. University of Regensburg, Regensburg, Germany; 2002.Google Scholar
  9. Vielva L, Santamaria I, Pantaleon C, Ibanez J, Erdogmus D: Estimation of the mixing matrix for underdetermined blind source separation using spectral estimation techniques. Proceedings of 11th European Signal Processing Conference (EUSIPCO '02), September 2002, Toulouse, France 1: 557-560.Google Scholar
  10. Waheed K, Salem FM: Algebraic overcomplete independent component analysis. Proceedings of International Workshop on Independent Component Analysis and Blind Signal Separation (ICA '03), April 2003, Nara, Japan 1077-1082.Google Scholar
  11. Yilmaz Ö, Rickard S: Blind separation of speech mixtures via time-frequency masking. IEEE Transactions on Signal Processing 2004,52(7):1830-1847. 10.1109/TSP.2004.828896MathSciNetView ArticleGoogle Scholar
  12. Bofill P: Underdetermined blind separation of delayed sound sources in the frequency domain. Neurocomputing 2003,55(3-4):627-641. 10.1016/S0925-2312(02)00631-8View ArticleGoogle Scholar
  13. Winter S, Sawada H, Araki S, Makino S: Overcomplete BSS for convolutive mixtures based on hierarchical clustering. Proceedings of International Workshop on Independent Component Analysis and Blind Signal Separation (ICA '04), September 2004, Granada, Spain 652-660.View ArticleGoogle Scholar
  14. Winter S, Sawada H, Makino S: On real and complex valued L1-norm minimization for overcomplete blind source separation. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA '05), October 2005, New Paltz, NY, USA 86-89.Google Scholar
  15. Hastie T, Tibshirani R, Friedman J: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics. Springer, New York, NY, USA; 2002.Google Scholar
  16. Sturm JF: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 1999,11(1):625-653. special issue on Interior Point Methods 10.1080/10556789908805766MathSciNetView ArticleGoogle Scholar
  17. Vielva L, Erdogmus D, Principe JC: Underdetermined blind source separation using a probabilistic source sparsity model. Proceedings of International Workshop on Independent Component Analysis and Blind Signal Separation (ICA '01), December 2001, San Diego, Calif, USA 675-679.Google Scholar
  18. Kellermann W, Buchner H: Wideband algorithms versus narrowband algorithms for adaptive filtering in the DFT domain. Proceedings of the Asilomar Conference on Signals, Systems and Computers, November 2003, Pacific Grove, Calif, USA 2: 1278-1282.Google Scholar
  19. Sawada H, Araki S, Mukai R, Makino S: Blind extraction of a dominant source signal from mixtures of many sources. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 3: 61-64.Google Scholar
  20. Murtagh F: Comments on 'Parallel algorithms for hierarchical clustering and cluster validity'. IEEE Transactions on Pattern Analysis and Machine Intelligence 1992,14(10):1056-1057. 10.1109/34.159908View ArticleGoogle Scholar
  21. Lewicki MS, Sejnowski TJ: Learning overcomplete representations. Neural Computation 2000,12(2):337-365. 10.1162/089976600300015826View ArticleGoogle Scholar
  22. Takigawa I, Kudo M, Toyama J:Performance analysis of minimum -norm solutions for underdetermined source separation. IEEE Transactions on Signal Processing 2004,52(3):582-591. 10.1109/TSP.2003.822284MathSciNetView ArticleGoogle Scholar
  23. Malioutov DM, Çetin M, Willsky AS: Optimal sparse representations in general overcomplete bases. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 2: 793-796.Google Scholar
  24. Pruessner A, Bussieck MR, Dirkse SP, Meeraus A: Conic programming in GAMS. INFORMS Annual Meeting, October 2003, Atlanta, Ga, USA 19-22.Google Scholar
  25. Araki S, Sawada H, Mukai R, Makino S: A novel blind source separation method with observation vector clustering. Proceedings of International Workshop on Acoustic Echo and Noise Control (IWAENC '05), September 2005, Eindhoven, The Netherlands 117-120.Google Scholar
  26. Févotte C, Gribonval R, Vincent E: BSS_EVAL toolbox user guide—Revision 2.0. In Tech. Rep. 1706. IRISA, Rennes, France; April 2005.Google Scholar
  27. Vincent E, Gribonval R, Févotte C: Performance measurement in blind audio source separation. IEEE Transactions on Audio, Speech and Language Processing 2006,14(4):1462-1469.View ArticleGoogle Scholar

Copyright

© Stefan Winter et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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