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A maximum likelihood approach to nonlinear blind source separation

  • Part IV: Signal Processing: Blind Source Separation, Vector Quantization, and Self-Organization
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Artificial Neural Networks — ICANN'97 (ICANN 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1327))

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Abstract

In the basic signal model of blind source separation (BSS), an unknown linear mixing process is assumed. While this ensures under mild conditions a sufficiently unique solution, it is desirable to extend the problem to nonlinear mixtures. Unfortunately the nonlinear case is much more difficult to handle, and brings serious indeterminacies to the solutions in the general case. In this paper we propose a new maximum likelihood approach to the nonlinear BSS problem. It is assumed that the source densities are known and that the mixing mapping is regularized. By finding a regular separating mapping which maximizes the likelihood, we show experimentally that the sources can often be separated.

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References

  1. J. Karhunen, A. Hyvärinen, R. Vigario, J. Hurri, and E. Oja, “Applications of neural blind separation to signal and image processing,” in Proc. 1997 Int. Conf. on Acoustics, Speech, and Signal Proc. ICASSP-97, (Munich, Germany), April 1997.

    Google Scholar 

  2. G. Burel, “Blind separation of sources: A nonlinear neural algorithm,” Neural Networks, vol. 5, no. 6, pp. 937–947, 1992.

    Google Scholar 

  3. P. Pajunen, A. Hyvärinen, and J. Karhunen, “Nonlinear blind source separation by self-organizing maps,” in Progress in Neural Information Processing (ICONIP-96) (S. Amari et al., eds.), pp. 1207–1210, Springer, 1996.

    Google Scholar 

  4. A. Taleb and C. Jutten, “Nonlinear source separation: The post-nonlinear mixtures,” in Proc. European Symposium on Artificial Neural Networks (ESANN97), (Bruges, Belgium), pp. 279–284, April 1997.

    Google Scholar 

  5. H. Yang, S. Amari, and A. Cichocki, “Information back-propagation for blind separation of sources from non-linear mixtures,” in Proc. Int. Conf. on Neural Networks (ICNN'97), (Houston, USA), pp. 2141–2146, June 1997.

    Google Scholar 

  6. R. Hecht-Nielsen, “Replicator neural networks for universal optimal source coding,” Science, vol. 269, pp. 1860–1863, September 1995.

    Google Scholar 

  7. C. Bishop, M. Svensen, and C. Williams, “GTM: The generative topographic mapping.” To appear in Neural Computation, 1997.

    Google Scholar 

  8. P. Pajunen, “A competitive learning algorithm for separating binary sources,” in Proc. European Symposium on Artificial Neural Networks (ESANN'97), (Bruges, Belgium), pp. 255–260, April 1997.

    Google Scholar 

  9. A. Belouchrani and J.-F. Cardoso, “Maximum likelihood source separation for discrete sources,” in Signal Processing VII: Theories and Applications (Proc. of the EUSIPCO-94), (Edinburgh, Scotland), pp. 768–771, Elsevier, September 1994.

    Google Scholar 

  10. G. Deco and W. Brauer, “Nonlinear higher-order statistical decorrelation by volume-conserving neural architectures,” Neural Networks, vol. 8, no. 4, pp. 525–535, 1995.

    Google Scholar 

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Wulfram Gerstner Alain Germond Martin Hasler Jean-Daniel Nicoud

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© 1997 Springer-Verlag Berlin Heidelberg

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Pajunen, P., Karhunen, J. (1997). A maximum likelihood approach to nonlinear blind source separation. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020210

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  • DOI: https://doi.org/10.1007/BFb0020210

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63631-1

  • Online ISBN: 978-3-540-69620-9

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