Skip to main content

Gaussian Processes for Source Separation in Overdetermined Bilinear Mixtures

  • Conference paper
  • First Online:
Latent Variable Analysis and Signal Separation (LVA/ICA 2017)

Abstract

In this work, we consider the nonlinear Blind Source Separation (BSS) problem in the context of overdetermined Bilinear Mixtures, in which a linear structure can be employed for performing separation. Based on the Gaussian Process (GP) framework, two approaches are proposed: the predictive distribution and the maximization of the marginal likelihood. In both cases, separation can be achieved by assuming that the sources are Gaussian and temporally correlated. The results with synthetic data are favorable to the proposal.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Comon, P., Jutten, C.: Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press, Oxford (2010)

    Google Scholar 

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

    Article  Google Scholar 

  3. Hosseini, S., Jutten, C.: On the separability of nonlinear mixtures of temporally correlated sources. IEEE Sig. Process. Lett. 10(2), 43–46 (2003)

    Article  Google Scholar 

  4. 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. 2687, pp. 241–248. Springer, Heidelberg (2003). doi:10.1007/3-540-44869-1_31

    Chapter  Google Scholar 

  5. Merrikh-Bayat, F., Babaie-Zadeh, M., Jutten, C.: Linear-quadratic blind source separating structure for removing show-through in scanned documents. Int. J. Doc. Anal. Recogn. (IJDAR) 14(4), 319–333 (2011)

    Article  Google Scholar 

  6. Duarte, L.T., Jutten, C.: Design of smart ion-selective electrode arrays based on source separation through nonlinear independent component analysis. Oil Gas Sci. Technol. 69(2), 293–306 (2014)

    Article  Google Scholar 

  7. Abed-Meraim, K., Belouchiani, A., Hua, Y.: Blind identification of a linear-quadratic mixture of independent components based on joint diagonalization procedure. IEEE ICASSP 5, 2718–2721 (1996)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Duarte, L.T., Ando, R.A., Attux, R., Deville, Y., Jutten, C.: Separation of sparse signals in overdetermined linear-quadratic mixtures. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds.) LVA/ICA 2012. LNCS, vol. 7191, pp. 239–246. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28551-6_30

    Chapter  Google Scholar 

  10. Ando, R.A., Duarte, L.T., Attux, R.R.F.: Blind source separation for overdetermined linear quadratic mixtures of bandlimited signals. In: IEEE International Telecommunications Symposium (ITS) (2014)

    Google Scholar 

  11. Rasmussen, C.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)

    MATH  Google Scholar 

  12. Deville, Y., Duarte, L.T.: An overview of blind source separation methods for linear-quadratic and post-nonlinear mixtures. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds.) LVA/ICA 2015. LNCS, vol. 9237, pp. 155–167. Springer, Heidelberg (2015). doi:10.1007/978-3-319-22482-4_18

    Google Scholar 

  13. Price, K., Storn, R., Lampinen, J.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Heidelberg (2005)

    MATH  Google Scholar 

Download references

Acknowledgements

This work was partly supported by FAPESP (2013/14185-2, 2015/23424-6), CNPq and ERC project 2012-ERC-AdG-320684 CHESS.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Denis G. Fantinato .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Fantinato, D.G., Duarte, L.T., Rivet, B., Ehsandoust, B., Attux, R., Jutten, C. (2017). Gaussian Processes for Source Separation in Overdetermined Bilinear Mixtures. In: Tichavský, P., Babaie-Zadeh, M., Michel, O., Thirion-Moreau, N. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2017. Lecture Notes in Computer Science(), vol 10169. Springer, Cham. https://doi.org/10.1007/978-3-319-53547-0_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-53547-0_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53546-3

  • Online ISBN: 978-3-319-53547-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics