Skip to main content
SpringerLink
Log in

Source number estimation and separation algorithms of underdetermined blind separation

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

Abstract

Recently, sparse component analysis (SCA) has become a hot spot in BSS research. Instead of independent component analysis (ICA), SCA can be used to solve underdetermined mixture efficiently. Two-step approach (TSA) is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However, the estimation of the source number is an obstacle. In this paper, a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that, the sources are recovered by the shortest path method (SPM). Simulations show the availability and robustness of the proposed method.

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

Access this article

Log in via an institution

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. He Z S, Xie S L, Fu Y L. Sparse representation and blind source separation of ill-posed mixtures. Sci China Ser F-Inf Sci, 2006, 49(5): 639–652

    Article  MathSciNet  Google Scholar 

  2. Hyvarinen A, Oja E. Independent component analysis: algorithms and applications. Neural Netw, 2000, 13(4–5): 411–430

    Article  Google Scholar 

  3. Tan H Z, Chow T W S. Blind identification of quadratic nonlinear models using neural networks with higher order cumulants. IEEE Trans Ind Electron, 2000, 47(3): 687–696

    Article  Google Scholar 

  4. Liu Y D, Zhou Z T, Hu D W, et al. A novel method for spatio-temporal pattern analysis of brain fMRI data. Sci China Ser FInf Sci, 2005, 48(2): 151–160

    Article  Google Scholar 

  5. Xie S L, He Z S, Fu Y L. A note on Stone’s conjecture of blind separation. Neural Comput, 2005, 17: 245–319

    Article  Google Scholar 

  6. Li Y Q, Amari S, Cichocki A, et al. Underdetermined blind source separation based on sparse representation. IEEE Trans Sig Proc, 2006, 54(2): 423–437

    Article  Google Scholar 

  7. Belouchrani A, Cardoso J F. Maximum likelihood source separation for discrete sources. In: Proc EUSIPCO. Edinburgh, 1994. 768–771

  8. Zibulevsky M, Pearlmutter B A. Blind source separation by sparse decomposition in a signal dictionary. Neural Comput, 2001, 13(4): 863–882

    Article  MATH  Google Scholar 

  9. Bofill P, Zibulevsky M. Underdetermined source separation using sparse representation. Sig Proc, 2001, 81: 2353–2362

    Article  MATH  Google Scholar 

  10. Li Y Q, Cichocki A, Amari S. Analysis of sparse representation and blind source separation. Neural Comput, 2004, 16(6): 1193–1234

    Article  MATH  Google Scholar 

  11. Lewicki M S, Sejnowski T J. Learning overcomplete representations. Neural Comput, 2000, 12: 337–365

    Article  Google Scholar 

  12. He Z S, Xie S L, Ding S X, et al. Convolutive blind source separation in the frequency domain based on sparse representation. IEEE Trans Audio Speech Lang Proc, 2007, 15: 1551–1563

    Article  Google Scholar 

  13. He Z S, Xie S L, Zhang L Q, et al. A note on Lewicki-Sejnowski gradient for learning overcomplete representations. Neural Comput, 2008, 20(3): 636–643

    Article  MATH  MathSciNet  Google Scholar 

  14. Wax M, Kailath T. Detection of signals by information theoretic criteria. IEEE Trans ASSP, 1985, 33(2): 276–280

    Article  MathSciNet  Google Scholar 

  15. Ye J M, Zhu X L, Zhang X D. Adaptive blind separation with an unknown number of sources. Neural Comput, 2004, 16(8): 1641–1660

    Article  MATH  Google Scholar 

  16. Zhang H Y, Jia P, Shi X Z. Determination of the number of source signals in blind source separation by singular value decomposition (in Chinese). J Shanghai Jiaotong Univ, 2001, 35(8): 1155–1158

    Google Scholar 

  17. Li G B, Xu S M. Blind source separation based on signal number estimation (in Chinese). J Syst Simul, 2006, 18(2): 485–488

    Google Scholar 

  18. Zhang Y, Ke H Y, Wen B Y, et al. A new method to estimate signal number by echo’s phase(in Chinese). Wuhan Univ J (Nat Sci Ed,), 2003, 49(1): 137–140

    Google Scholar 

  19. Zhang X H, Zhang A Q, Sun J P. A blind method for estimating the number of signal sources (in Chinese). Syst Eng Electr, 2001, 23(9): 9–11

    Google Scholar 

  20. He Z S, Xie S L, Fu Y L. Sparsity analysis of signals. Progress Nat Sci, 2006, 16(8): 879–884

    Article  MATH  MathSciNet  Google Scholar 

  21. Lv Q, Zhang X D. A unified method for blind separation of sparse sources with unknown source number. IEEE Sig Proc Lett, 2006, 13: 49–51

    Article  Google Scholar 

  22. Yang L B, Gao Y Y. The theory and application of fuzzy mathematics (in Chinese). Guangzhou: South China University of Technology Press, 2002. 86–125

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    ZuYuan Yang, BeiHai Tan, GuoXu Zhou & JinLong Zhang

Authors
  1. ZuYuan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. BeiHai Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. GuoXu Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. JinLong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to BeiHai Tan.

Additional information

Supported by Key Program of the National Natural Science Foundation of China (Grant No. U0635001), the National Natural Science Foundation of China (Grant Nos. 60674033 and 60774094)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, Z., Tan, B., Zhou, G. et al. Source number estimation and separation algorithms of underdetermined blind separation. Sci. China Ser. F-Inf. Sci. 51, 1623–1632 (2008). https://doi.org/10.1007/s11432-008-0138-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-008-0138-6

Keywords

Search

Navigation