Skip to main content
Springer Nature Link
Log in

Sparse representation and blind source separation of ill-posed mixtures

  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

Bofill et al. discussed blind source separation (BSS) of sparse signals in the case of two sensors. However, as Bofill et al. pointed out, this method has some limitation. The potential function they introduced is lack of theoretical basis. Also the method could not be extended to solve the problem in the case of more than three sensors. In this paper, instead of the potential function method, a K-PCA method (combining K-clustering with PCA) is proposed. The new method is easy to be used in the case of more than three sensors. It is easy to be implemented and can provide accurate estimation of mixing matrix. Some criterion is given to check the effect of the mixing matrix A. Some simulations illustrate the availability and accuracy of the method we proposed.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tong L, Liu R, Soon V C, et al. Indeterminacy and identifiability of blind identification. IEEE Trans Circuits and Systems, 1991, 38(5): 499–506

    Article  MATH  Google Scholar 

  2. Cao X R, Liu RW. General approach to blind source separation. IEEE Trans Signal Processing, 1996, 44: 562–571

    Article  Google Scholar 

  3. Li Y Q, Wang J. Blind extraction of singularly mixed source signals. IEEE Trans Signal Processing, 2000, 11: 1413–1422

    Google Scholar 

  4. Zhang J L, Xie S L, He Z S. Separability theory for blind signal separation. Acta Automatica Sinica, 2004, 30(3): 337–344

    MathSciNet  Google Scholar 

  5. Hyvarinen A. A fast and robust fixed-point algorithms for independent component analysis. IEEE Trans Neural Networks, 1999, 10(3): 626–634

    Article  Google Scholar 

  6. Comon P. Independent component analysis, a new concept? Signal Processing, 1992, 36(3): 287–314

    Article  Google Scholar 

  7. Cardoso J F. Source separation using higher order-moments. In: Proc ICASSP89, Glasgow, Scotland. 1989, 4: 2109–2112

    Google Scholar 

  8. Bell A, Sejnowski T. An information maximization approach to blind separation and blind deconvolution. Neural Computation, 1995, 7: 1129–1159

    Google Scholar 

  9. Yang H H. Adaptive on-line learning algorithms for blind separation-maximum entropy and minimum mutual information. Neural Computation, 1997, 9: 1457–1482

    Article  Google Scholar 

  10. Amari S, Cichocki A, Yang H H. A new algorithm for blind source separation. In: Advances in Neural Information Processing (Proc. NIPS’95). Cambridge, MA: MIT Press, 1996. 757–763

    Google Scholar 

  11. He Z Y, Liu J, Yang L X. An ICA and EC based approach for blind equalization and channel parameter estimation. Sci China Ser E-Tech Sci, 2000, 43(1): 1–8

    Article  MATH  Google Scholar 

  12. He Z Y, Yang L X, Liu J. Blind source separation using cluster-based multivariate density estimation algorithm. IEEE Trans Signal Processing, 2000, 48(2): 575–579

    Article  Google Scholar 

  13. Zhang X D, Zhu X L, Bao Z. Blind signal separation based on learning in stages. Sci China Ser F-Inf Sci, 2003, 46(1): 31–44

    Article  MATH  Google Scholar 

  14. Bofill P, Zibulevsky M. Underdetermined blind source separation using sparse representations, Signal Processing, 2001, 81(11): 2353–2362

    Article  MATH  Google Scholar 

  15. Li Y Q, Cichocki A, Amari S. Analysis of sparse representation and blind source separation. Neural Computation, 2004, 16: 1193–1234

    Article  MATH  Google Scholar 

  16. Zibulevsky M, Pearmutter B A. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation, 2001, 13: 863–882

    Article  MATH  Google Scholar 

  17. Pearlmutter B A, Potluru V K. Sparse separation: Principles and tricks. In: Proc SPIE volume 5102, “Independent Component Analyses, Wavelets, and Neural Networks”, Orlando, FL: SPIE Org., 2003. 1–4

    Chapter  Google Scholar 

  18. Lee T W, Lewicki M S, Girolami M, et al. Blind source separation of more sources than mixtures using over-complete representations. IEEE Signal Process Lett, 1999, 6(4): 87–90

    Article  Google Scholar 

  19. Lewiski M S, Sejnowski T J. Learning overcomplete representations. Neural Comput, 2000, 12(2): 337–365

    Article  Google Scholar 

  20. Olshause B A N, Field D J. Sparse coding with an overcomplete basis set: a strategy employed by V1? Vision Res, 1997, 37: 3311–3325

    Article  Google Scholar 

  21. Zibulevsky M, Pearlmutter B A. Blind source separation by sparse decomposition. Technicial Report No. CS99-1. University of New Mexico, Albuquerque, July 1999, http://www.cs.unm.edu/:_bap/papers/sparse-ica-99a.ps.gz

    Google Scholar 

  22. Wang X R, Wang G S. Applied Multi-variables Statistical Analysis (in Chinese). Shanghai: Shanghai Scientific Press, 1990

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronics & Information Engineering, South China University of Technology, Guangzhou, 510640, China

    He Zhaoshui, Xie Shengli & Fu Yuli

Authors
  1. He Zhaoshui
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Xie Shengli
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Fu Yuli
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Xie Shengli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

He, Z., Xie, S. & Fu, Y. Sparse representation and blind source separation of ill-posed mixtures. SCI CHINA SER F 49, 639–652 (2006). https://doi.org/10.1007/s11432-006-2020-8

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-006-2020-8

Keywords