ICISP 2012: Image and Signal Processing pp 157-165 | Cite as

Nonlinear Blind Source Separation Applied to a Simple Bijective Model

  • Shahram Hosseini
  • Yannick Deville
  • Sonia El Amine
  • Hicham Saylani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7340)

Abstract

This paper deals with nonlinear Blind Source Separation (BSS) applied to a simple bijective “toy” model. Our objective is to better understand the difficulties encountered in nonlinear BSS, especially when estimating the parameters of mixing or separating structures. The results of this study and the proposed solutions may then be used by the BSS researchers dealing with actual nonlinear physical models. The simulation results confirm the usefulness of our proposed solutions.

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References

  1. 1.
    Taleb, A., Jutten, C.: Source separation in post-nonlinear mixtures. IEEE Trans. on Signal Processing 47(10), 2807–2820 (1999)CrossRefGoogle Scholar
  2. 2.
    Jutten, C., Babaie-Zadeh, M., Hosseini, S.: Three easy ways for separating nonlinear mixtures? Signal Processing 84(2), 217–229 (2004)MATHCrossRefGoogle Scholar
  3. 3.
    Almeida, L.B.: MISEP - linear and nonlinear ICA based on mutual information. Journal of Machine Learning Research 4, 1297–1318 (2003)Google Scholar
  4. 4.
    Zhang, K., Chan, L.: Kernel-Based Nonlinear Independent Component Analysis. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 301–308. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Eriksson, J., Koivunen, V.: Blind identifiability of class of nonlinear instantaneous ICA models. In: Proc. of EUSIPCO 2002, Toulouse, vol. 2, pp. 7–10 (September 2002)Google Scholar
  6. 6.
    Hosseini, S., Deville, Y.: Blind Maximum Likelihood Separation of a Linear-Quadratic Mixture. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 694–701. Springer, Heidelberg (2004), ERRATUM: http://arxiv.org/abs/1001.0863 CrossRefGoogle Scholar
  7. 7.
    Duarte, L.T., Jutten, C.: Blind Source Separation of a Class of Nonlinear Mixtures. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 41–48. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Taleb, A.: A generic framework for blind source separation in structured nonlinear models. IEEE Trans. Sig. Proc. 50(8), 1819–1830 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pham, D.T., Garat, P.: Blind separation of mixtures of independent sources through a quasi maximum likelihood approach. IEEE Trans. Sig. Proc. 45(7), 1712–1725 (1997)MATHCrossRefGoogle Scholar
  10. 10.
    Pham, D.T.: Séparation aveugle de mélange instantanée de sources à l’aide de fonctions séparatrices ajustées. In: Proc. GRETSI 1997, pp. 969–972 (September 1997)Google Scholar
  11. 11.
    Nocedal, J., Wright, S.: Numerical optimization. Springer (2006)Google Scholar
  12. 12.
    Bishop, C.M.: Neural networks for pattern recognition, Oxford (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shahram Hosseini
    • 1
  • Yannick Deville
    • 1
  • Sonia El Amine
    • 1
  • Hicham Saylani
    • 2
  1. 1.Institut de Recherche en Astrophysique et PlanétologieUniversité de Toulouse, UPS-CNRS-OMPToulouseFrance
  2. 2.Laboratoire d’Electronique, de Traitement du Signal et de Modélisation Physique, Faculté des SciencesUniversité Ibnou ZohrAgadirMorocco

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