Skip to main content

Advertisement

Springer Nature Link
Log in

Underdetermined Blind Source Separation by Parallel Factor Analysis in Time-Frequency Domain

  • Published:
Cognitive Computation Aims and scope Submit manuscript

Abstract

This paper presents a new time-frequency approach to the underdetermined blind source separation using the parallel factor decomposition of third-order tensors. Without any constraint on the number of active sources at an auto-term time-frequency point, this approach can directly separate the sources as long as the uniqueness condition of parallel factor decomposition is satisfied. Compared with the existing two-stage methods where the mixing matrix should be estimated at first and then used to recover the sources, our approach yields better source separation performance in the presence of noise. Moreover, the mixing matrix can be estimated at the same time of the source separation process. Numerical simulations are presented to show the superior performance of the proposed approach to some of the existing two-stage blind source separation methods that use the time-frequency representation as well.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Comon P. Independent component analysis. A new concept? Signal Process. 1994;36:287–4.

    Article  Google Scholar 

  2. He Z, Xie S, Ding S, Cichocki A. Convolutive blind source separation in the frequency domain based on sparse representation. IEEE Trans Audio Speech Lang Process. 2007;15:1551–63.

    Article  Google Scholar 

  3. Levin DN. Performing nonlinear blind source separation with signal invariants. IEEE Trans Signal Process. 2010;58:2131–40.

    Article  Google Scholar 

  4. Moussaoui S, Brie D, Mohammad-Djafari A, Carteret C. Separation of non-negative mixture of non-negative sources using a Bayesian approach and MCMC sampling. IEEE Trans Signal Process. 2006;54:4133–45.

    Article  Google Scholar 

  5. Li Y, Amari S, Cichocki A, Ho DWC, Xie S. Underdetermined blind source separation based on sparse representation. IEEE Trans Signal Process. 2006;54:423–37.

    Article  Google Scholar 

  6. Georgiev P, Theis F, Cichocki A. Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Trans Neural Netw. 2005;16:992–6.

    Article  PubMed  Google Scholar 

  7. He Z, Cichocki A, Zdunek R, Xie S. Improved FOCUSS method with conjugate gradient iterations. IEEE Trans Signal Process. 2009;57:399–404.

    Article  Google Scholar 

  8. De Lathauwer L, Castaing J, Cardoso J-F. Fourth-order cumulant-based blind identification of underdetermined mixtures. IEEE Trans Signal Process. 2007;55:2965–73.

    Article  Google Scholar 

  9. De Lathauwer L, Castaing J. Blind identification of underdetermined mixtures by simultaneous matrix diagonalization. IEEE Trans Signal Process. 2008;56:1096–105.

    Article  Google Scholar 

  10. Ferreol A, Albera L, Chevalier P. Fourth-order blind identification of underdetermined mixtures of sources (FOBIUM). IEEE Trans Signal Process. 2005;53:1640–53.

    Article  Google Scholar 

  11. Aissa-El-Bey A, Linh-Trung N, Abed-Meraim K, Belouchrani A, Grenier Y. Underdetermined blind separation of nondisjoint sources in the time-frequency domain. IEEE Trans Signal Process. 2007;55:897–907.

    Article  Google Scholar 

  12. Peng D, Xiang Y. Underdetermined blind source separation based on relaxed sparsity condition of sources. IEEE Trans Signal Process. 2009;57:809–14.

    Article  Google Scholar 

  13. Linh-Trung N, Belouchrani A, Abed-Meraim K, Boashash B. Separating more sources than sensors using time-frequency distributions. EURASIP J Appl Signal Process. 2005.

  14. Xie S, Yang L, Yang J-M, Zhou G, Xiang Y. Time-frequency approach to underdetermined blind source separation. IEEE Trans Neural Netw Learn Syst. 2012;23:306–16.

    Article  Google Scholar 

  15. Gorodnitsky IF, Rao B. Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Trans Signal Process. 1997;45:600–16.

    Article  Google Scholar 

  16. Kiers HAL. Towards a standardized notation and terminology in multiway analysis. J Chemom. 2000;14:105–22.

    Article  CAS  Google Scholar 

  17. De Lathauwer L, Castaing J. Blind identification of underdetermined mixtures by simultaneous matrix diagonalization. IEEE Trans Signal Process. 2008;56:1096–105.

    Article  Google Scholar 

  18. Kruskal Joseph B. Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra Appl. 1977;18:95–138.

    Article  Google Scholar 

  19. Kruskal JB. Rank, decomposition, and uniqueness for 3-way and n-way arrays, Multiway data analysis. Amsterdam: North-Holland; 1989. p. 7–18.

    Google Scholar 

  20. Jiang Tao, Sidiropoulos. Kruskal’s permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints. N.D. IEEE Trans Signal Process 2004;52:2625–36.

  21. Kolda TG, Bader BW. Tensor decompositions and applications. SIAM Rev. 2009;51:455–500.

    Article  Google Scholar 

  22. De Lathauwer L. A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization. SIAM J Matrix Anal Appl 2006;28:642–66.

    Article  Google Scholar 

  23. Allen Ronald L, Mills Duncan W. Signal analysis: time, frequency, scale, and structure. New York: IEEE press, Wiley; 2004.

    Google Scholar 

  24. He Z, Cichocki A, Xie S, Choi K. Detecting the number of clusters in n-way probabilistic clustering. IEEE Trans Pattern Anal Machine Intell. 2010;32:2006–21.

    Article  PubMed  Google Scholar 

  25. Boudreaux-Bartels G, Parks T. Time-varying filtering and signal estimation using Wigner distribution synthesis techniques. IEEE Trans Acoust Speech Signal Process. 1986;34:442–51.

    Article  Google Scholar 

  26. Cichocki A, Amari S, Siwek K, Tanaka T, Phan AH. ICALAB toolboxes [Online]. Available: http://www.bsp.brain.riken.jp/ICALAB.

Download references

Acknowledgments

The work in this paper is partly supported by the National Natural Science Foundation of China under grants 61004054, 61103122, 61104053, and U1035001 and the Guangdong Natural Science Foundation (team project) under grant S2011030002886.

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, South China University of Technology, Guangzhou, 510640, China

    Liu Yang

  2. Faculty of Automation, Guangdong University of Technology, Guangzhou, 510006, China

    Jun Lv

  3. School of Information Technology, Deakin University, Burwood, VIC, 3125, Australia

    Yong Xiang

Authors
  1. Liu Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jun Lv
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Yong Xiang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Liu Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, L., Lv, J. & Xiang, Y. Underdetermined Blind Source Separation by Parallel Factor Analysis in Time-Frequency Domain. Cogn Comput 5, 207–214 (2013). https://doi.org/10.1007/s12559-012-9177-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12559-012-9177-9

Keywords