Skip to main content
SpringerLink
Log in

Robust Blind Source Separation Utilizing Second and Fourth Order Statistics

  • Conference paper
  • First Online:
Artificial Neural Networks — ICANN 2002 (ICANN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2415))

Included in the following conference series:

Abstract

We introduce identifiability conditions for the blind source separation (BSS) problem, combining the second and fourth order statistics. We prove that under these conditions, well known methods (like eigen-value decomposition and joint diagonalization) can be applied with probability one, i.e. the set of parameters for which such a method doesn’t solve the BSS problem, has a measure zero.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Belouchrani and A. Cichocki A. “Robust whitening procedure in blind separation context”. Electronics Letters, Vol. 36 No. 24, pp. 2050–2051, 2000.

    Article  Google Scholar 

  2. A. Belouchrani, K. A. Meraim, J.-P. Cardoso and E. Moulines “A blind source separation technique using second order statistics.” IEEE Trans. on Signal Processing, Vol. 45, no. 2, pp. 434–44, Feb. 1997

    Article  Google Scholar 

  3. J.-F. Cardoso, “High-order contrasts for independent component analysis” Neural Computation, vol. 11, no 1, pp. 157–192, Jan. 1999.

    Article  MathSciNet  Google Scholar 

  4. C. Chang, Z. Ding, S. F. Yau and F. H. Y. Chan“A matrix-pencil approach to blind separation of colored nonstationary signals”. IEEE Trans. Signal Proc., Vol. 48, No. 3, pp. 900–907, Mar. 2000.

    Article  Google Scholar 

  5. C. Chang, S.F. Yau, P. Kwok, F.H.Y. Chan, F.K. Lam, Uncorrelated and component analysis for blind source separation, Circuits Systems and Signal Processsing, Vol. 18, No. 3, pp. 225–239, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Cichocki and S. Amari. Adaptive Blind Signal and Image Processing. John Wiley, Chichester, 2002.

    Google Scholar 

  7. A. Cichocki, and R. Thawonmas “ On-line algorithm for blind signal extraction of arbitrarily distributed, but temporally correlated sources using second order statistics”. Neural Processing Letters Vol. 12, pp. 91–98, Aug. 2000.

    Google Scholar 

  8. I. Gorodnitsky and A. Belouchrani, “Joint cumulant and correlation based signal separation with application of EEG data analysis”, Proc. 3-rd Int. Conf. on Independent Component Analysis and Signal Separation, San Diego, California, Dec. 9-13, 2001, pp. 475–480.

    Google Scholar 

  9. A. Edelman, T. A. Arias and A. T. Smith“The geometry of algorithms with orthogonality constraints”. SIAM J. Matrix Anal. Appl., Vo. 20, No. 2, pp. 303–353, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  10. G. H. Golub and C. F. Van Loan Matrix Computation. J. Hopkins Univ. Press, 1989.

    Google Scholar 

  11. A. Hyvarinen, J. Karhunen and E. Oja, “Independent Component Analysis”, John Wiley & Sons, 2001.

    Google Scholar 

  12. C. L. Nikias and A. Petropulu“Higher-order spectra analysis. A nonlinear signal processing framework”, Prentice Hall Signal Processing Series, 1993.

    Google Scholar 

  13. L. Tong, R. Liu, V.C. Soon and Y.F. Huang, Indeterminacy and Identifiability of Blind Identification, IEEE Transactions on Circuits and Systems, Vol. 38, No. 5, pp. 499–509, May 1991.

    Article  MATH  Google Scholar 

  14. L. Tong, Y. Inouye and R. Liu “ A finite-step global algorithm for the parameter estimation of multichannel MA processes”. IEEE Trans. Signal Proc., 40(10): 2547–2558, 1992.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RIKEN, Brain Science Institute, Wako-shi, Saitama, 351-0198, Japan

    Pando Georgiev

  2. Sofia University “St. Kl. Ohridski”, Bulgaria

    Pando Georgiev

  3. RIKEN, Brain Science Institute, Wako-shi, Saitama, 351-0198, Japan

    Andrzej Cichocki

  4. Warsaw University of Technology, Poland

    Andrzej Cichocki

Authors
  1. Pando Georgiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrzej Cichocki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. ETS Informática, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    José R. Dorronsoro

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Georgiev, P., Cichocki, A. (2002). Robust Blind Source Separation Utilizing Second and Fourth Order Statistics. In: Dorronsoro, J.R. (eds) Artificial Neural Networks — ICANN 2002. ICANN 2002. Lecture Notes in Computer Science, vol 2415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46084-5_188

Download citation

  • DOI: https://doi.org/10.1007/3-540-46084-5_188

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44074-1

  • Online ISBN: 978-3-540-46084-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation