Skip to main content

The Complex Version of the Minimum Support Criterion

  • Conference paper
Independent Component Analysis and Signal Separation (ICA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4666))

Abstract

This paper addresses the problem of the blind signal extraction of sources by means of an information theoretic and geometric criterion. Our main result is the extension of the minimum support criterion to the case of mixtures of complex signals. This broadens the scope of its possible applications in several fields, such as communications.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Donoho, D.: On minimum entropy deconvolution. In: Findley, D.F. (ed.) Applied Time Series Analysis II, pp. 565–608. Academic Press, New York (1981)

    Google Scholar 

  2. Blachman, N.M.: The convolution inequality for entropy powers. IEEE Trans. on Information Theory IT-11, 267–271 (1965)

    Article  MathSciNet  Google Scholar 

  3. Comon, P.: Independent component analysis, a new concept? Signal Processing 3(36), 287–314 (1994)

    Article  Google Scholar 

  4. Cruces, S., Cichocki, A., Amari, S-i.: From blind signal extraction to blind instantaneous signal separation: criteria, algorithms and stability. IEEE Trans. on Neural Networks 15(4), 859–873 (2004)

    Article  Google Scholar 

  5. Bercher, J.-F., Vignat, C.: A Renyi entropy convolution inequality with application. In: Proc. of EUSIPCO, Toulouse, France (2002)

    Google Scholar 

  6. Erdogmus, D., Principe, J.C., Vielva, L.: Blind deconvolution with minimum Renyi’s entropy. In: Proc. of EUSIPCO, Toulouse, France, vol. 2, pp. 71–74 (2002)

    Google Scholar 

  7. Pham, D.T.: Blind separation of instantaneous mixture of sources based on order statistics. IEEE Trans. on Signal Processing 48(2), 363–375 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cruces, S., Durán, I.: The minimum support criterion for blind signal extraction. In: Proc. of the int. conf. on Independent Component Analysis and Blind Signal Separation, Granada, Spain, pp. 57–64 (2004)

    Google Scholar 

  9. Vrins, F., Verleysen, M., Jutten, C.: SWM: A class of convex contrasts for source separation. In: Proc. of the Int. Conf. on Acoustics, Speech and Signal Processing, Philadelphia (USA), vol. V, pp. 161–164 (2005)

    Google Scholar 

  10. Cruces, S., Sarmiento, A.: Criterion for blind simultaneous extraction of signals with clear boundaries. Electronics Letters 41(21), 1195–1196 (2005)

    Article  Google Scholar 

  11. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley series in telecommunications. John Wiley, Chichester (1991)

    MATH  Google Scholar 

  12. Gardner, R.J.: The Brunn-Minkowski Inequality. Bulletin of the American Mathematical Society 39(3), 355–405 (2002)

    Article  MATH  Google Scholar 

  13. Henstock, R., Macbeath, A.M.: On the measure of sum-sets. I. The theorems of Brunn, Minkowski, and Lusternik. In: Proceedings of the London Mathematical Society, third series, vol. 3, pp. 182–194 (1953)

    Google Scholar 

  14. Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)

    Google Scholar 

  15. Chan, T.M.: Optimal output-sensitive convex hull algorithms in two and three dimensions. Discrete and Computational Geometry 16, 361–368 (1996)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Mike E. Davies Christopher J. James Samer A. Abdallah Mark D Plumbley

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cruces, S., Sarmiento, A., Durán, I. (2007). The Complex Version of the Minimum Support Criterion. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74494-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74493-1

  • Online ISBN: 978-3-540-74494-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics