Open Access

Geometrical Interpretation of the PCA Subspace Approach for Overdetermined Blind Source Separation

EURASIP Journal on Advances in Signal Processing20062006:071632

https://doi.org/10.1155/ASP/2006/71632

Received: 25 January 2005

Accepted: 26 August 2005

Published: 20 March 2006

Abstract

We discuss approaches for blind source separation where we can use more sensors than sources to obtain a better performance. The discussion focuses mainly on reducing the dimensions of mixed signals before applying independent component analysis. We compare two previously proposed methods. The first is based on principal component analysis, where noise reduction is achieved. The second is based on geometric considerations and selects a subset of sensors in accordance with the fact that a low frequency prefers a wide spacing, and a high frequency prefers a narrow spacing. We found that the PCA-based method behaves similarly to the geometry-based method for low frequencies in the way that it emphasizes the outer sensors and yields superior results for high frequencies. These results provide a better understanding of the former method.

[12345678910111213141516]

Authors’ Affiliations

(1)
Department of Multimedia Communication and Signal Processing, University of Erlangen-Nuremberg
(2)
NTT Communication Science Laboratories, NTT Corporation

References

  1. Hyvärinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.View ArticleGoogle Scholar
  2. Joho M, Mathis H, Lambert RH: Overdetermined blind source separation: using more sensors than source signals in a noisy mixture. Proceedings of 2nd International Conference on Independent Component Analysis and Blind Signal Separation (ICA '00), June 2000, Helsinki, Finland 81-86.Google Scholar
  3. Westner A, Bove VM Jr.: Blind separation of real world audio signals using overdetermined mixtures. Proceedinds of 1st International Conference on Independent Component Analysis and Blind Signal Separation (ICA '99), January 1999, Aussois, FranceGoogle Scholar
  4. Koutras A, Dermatas E, Kokkinakis G: Improving simultaneous speech recognition in real room environments using overdetermined blind source separation. Proceedings of 7th European Conference on Speech Communication and Technology (Eurospeech '01), September 2001, Aalborg, Denmark 1009-1012.Google Scholar
  5. Asano F, Ikeda S, Ogawa M, Asoh H, Kitawaki N: Combined approach of array processing and independent component analysis for blind separation of acoustic signals. IEEE Transactions on Speech and Audio Processing 2003, 11(3):204-215. 10.1109/TSA.2003.809191View ArticleGoogle Scholar
  6. Sawada H, Araki S, Mukai R, Makino S: Blind source separation with different sensor spacing and filter length for each frequency range. Proceedings of 12th IEEE International Workshop on Neural Networks for Signal Processing (NNSP '02), September 2002, Martigny, Switzerland 465-474.View ArticleGoogle Scholar
  7. Winter S, Sawada H, Makino S: Geometrical understanding of the PCA subspace method for overdetermined blind source separation. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP~'03), April 2003, Hong Kong 2: 769-772.Google Scholar
  8. Sawada H, Mukai R, Araki S, Makino S: Frequency-domain blind source separation. In Speech Enhancement. Edited by: Benesty J, Makino S, Chen J. Springer, Berlin, Germany; 2005:299-327.View ArticleGoogle Scholar
  9. Bingham E, Hyvärinen A: A fast fixed-point algorithm for independent component analysis of complex valued signals. International Journal of Neural Systems 2000, 10(1):1-8.View ArticleGoogle Scholar
  10. Ikram MZ, Morgan DR: Exploring permutation inconsistency in blind separation of speech signals in a reverberant environment. Proceedinds of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 2: 1041-1044.Google Scholar
  11. 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
  12. Hyvärinen A, Särelä J, Vigário R: Bumps and spikes: artifacts generated by independent component analysis with insufficient sample size. Proceedings of 1st International Workshop on Independent Component Analysis and Blind Signal Separation (ICA '99), January 1999, Aussois, France 425-429.Google Scholar
  13. Nadal JP, Korutcheva E, Aires F: Blind source separation in the presence of weak sources. Neural Networks 2000, 13(6):589-596. 10.1016/S0893-6080(00)00041-1View ArticleGoogle Scholar
  14. Pillai SU: Array Signal Processing. Springer, New York, NY, USA; 1989.View ArticleGoogle Scholar
  15. Real World Computing Partnership : RWCP sound scene database in real acoustic environments. http://tosa.mri.co.jp/sounddb/indexe.htm
  16. Bronstein IN, Semendjajew KA, Musiol G, Mühlig H: Taschenbuch der Mathematik. 3rd edition. Harri Deutsch, Frankfurt am Main, Germany; 1997.Google Scholar

Copyright

© Winter et al. 2006

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.