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Blind Source Separation of Overdetermined Linear-Quadratic Mixtures

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6365))

Abstract

This work deals with the problem of source separation in overdetermined linear-quadratic (LQ) models. Although the mixing model in this situation can be inverted by linear structures, we show that some simple independent component analysis (ICA) strategies that are often employed in the linear case cannot be used with the studied model. Motivated by this fact, we consider the more complex yet more robust ICA framework based on the minimization of the mutual information. Special attention is given to the development of a solution that be as robust as possible to suboptimal convergences. This is achieved by defining a method composed of a global optimization step followed by a local search procedure. Simulations confirm the effectiveness of the proposal.

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References

  1. Jutten, C., Karhunen, J.: Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures. International Journal of Neural Systems 14, 267–292 (2004)

    Article  Google Scholar 

  2. Duarte, L.T., Jutten, C., Moussaoui, S.: A Bayesian nonlinear source separation method for smart ion-selective electrode arrays. IEEE Sensors Journal 9(12), 1763–1771 (2009)

    Article  Google Scholar 

  3. Bedoya, G.: Nonlinear blind signal separation for chemical solid-state sensor arrays. PhD thesis, Universitat Politecnica de Catalunya (2006)

    Google Scholar 

  4. Hyvärinen, A., Pajunen, P.: Nonlinear independent component analysis: existence and uniqueness results. Neural Networks 12, 429–439 (1999)

    Article  Google Scholar 

  5. Hosseini, S., Deville, Y.: Blind separation of linear-quadratic mixtures of real sources using a recurrent structure. In: Mira, J., Álvarez, J.R. (eds.) IWANN 2003. LNCS, vol. 2686, Springer, Heidelberg (2003)

    Google Scholar 

  6. Deville, Y., Hosseini, S.: Recurrent networks for separating extractable-target nonlinear mixtures. part i: Non-blind configurations. Signal Processing 89, 378–393 (2009)

    Article  MATH  Google Scholar 

  7. Duarte, L.T., Jutten, C., Moussaoui, S.: Bayesian source separation of linear-quadratic and linear mixtures through a MCMC method. In: Proc. of the IEEE MLSP (2009)

    Google Scholar 

  8. Castella, M.: Inversion of polynomial systems and separation of nonlinear mixtures of finite-alphabet sources. IEEE Trans. on Sig. Proc. 56(8), 3905–3917 (2008)

    Article  MathSciNet  Google Scholar 

  9. Abed-Meraim, K., Belouchiani, A., Hua, Y.: Blind identification of a linear-quadratic mixture of independent components based on joint diagonalization procedure. In: Proceedings of the IEEE ICASSP 1996, vol. 5, pp. 2718–2272 (1996)

    Google Scholar 

  10. Comon, P., Jutten, C. (eds.): Handbook of blind source separation, independent component analysis and applications. Academic Press, Elsevier (2010)

    Google Scholar 

  11. Zhang, L.Q., Cichocki, A., Amari, S.: Natural gradient algorithm for blind separation of overdetermined mixture with additive noise. IEEE Signal Processing Letters 6(11), 293–295 (2009)

    Article  Google Scholar 

  12. Babaie-Zadeh, M., Jutten, C., Nayebi, K.: Differential of the mutual information. IEEE Signal Processing Letters 11(1), 48–51 (2004)

    Article  Google Scholar 

  13. Pham, D.T.: Fast algorithm for estimating mutual information, entropies and score functions. In: Proceedings of the ICA, pp. 17–22 (2003)

    Google Scholar 

  14. Darbellay, G.A., Vajda, I.: Estimation of the information by an adaptive partitioning of the observation space. IEEE Trans. on Inf. Theory 45(4), 1315–1321 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. de Castro, L.N., Timmis, J.: Artificial Immune Systems: A New Computational Approach. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  16. Moddemeijer, R.: On estimation of entropy and mutual information of continuous distributions. Signal Processing 16(3), 233–248 (1989)

    Article  MathSciNet  Google Scholar 

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Duarte, L.T., Suyama, R., Attux, R., Deville, Y., Romano, J.M.T., Jutten, C. (2010). Blind Source Separation of Overdetermined Linear-Quadratic Mixtures. In: Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2010. Lecture Notes in Computer Science, vol 6365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15995-4_33

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  • DOI: https://doi.org/10.1007/978-3-642-15995-4_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15994-7

  • Online ISBN: 978-3-642-15995-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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