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Separation of Sparse Signals in Overdetermined Linear-Quadratic Mixtures

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7191))

Abstract

In this work, we deal with the problem of nonlinear blind source separation (BSS). We propose a new method for BSS in overdetermined linear-quadratic (LQ) mixtures. By exploiting the assumption that the sources are sparse in a transformed domain, we define a framework for canceling the nonlinear part of the mixing process. After that, separation can be conducted by linear BSS algorithms. Experiments with synthetic data are performed to assess the viability of our proposal.

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References

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

    Google Scholar 

  2. Romano, J.M.T., Attux, R.R.F., Cavalcante, C.C., Suyama, R.: Unsupervised signal processing: channel equalization and source separation. CRC Press (2011)

    Google Scholar 

  3. 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 

  4. Meganem, I., Deville, Y., Hosseini, S., Déliot, P., Briottet, X., Duarte, L.T.: Linear-quadratic and polynomial non-negative matrix factorization; application to spectral unmixing. In: Proc. of the 19th European Signal Processing Conference, EUSIPCO 2011 (2011)

    Google Scholar 

  5. 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 

  6. Comon, P.: Independent component analysis, a new concept? Signal Processing 36, 287–314 (1994)

    Article  MATH  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Merrikh-Bayat, F., Babaie-Zadeh, M., Jutten, C.: Linear-quadratic blind source separating structure for removing show-through in scanned documents. International Journal on Document Analysis and Recognition, 1–15 (2010)

    Google Scholar 

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

    Google Scholar 

  10. 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 

  11. 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 

  12. Abed-Meraim, K., Belouchrani, A., Hua, Y.: Blind identification of a linear-quadratic mixture of independent components based on joint diagonalization procedure. In: Proc. of the IEEE Inter. Conf. on Acous., Spee., and Signal Processing, ICASSP (1996)

    Google Scholar 

  13. Deville, Y., Hosseini, S.: Blind identification and separation methods for linear-quadratic mixtures and/or linearly independent non-stationary signals. In: Proc. of the 9th Int. Symp. on Sig. Proc. and its App., ISSPA (2007)

    Google Scholar 

  14. Duarte, L.T., Suyama, R., Attux, R., Deville, Y., Romano, J.M.T., Jutten, C.: Blind Source Separation of Overdetermined Linear-Quadratic Mixtures. In: Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds.) LVA/ICA 2010. LNCS, vol. 6365, pp. 263–270. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Elad, M.: Sparse and redundant representations from theory to applications in signal and image processing. Springer, Heidelberg (2010)

    Book  MATH  Google Scholar 

  16. Mohimani, H., Babaie-Zadeh, M., Jutten, C.: A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm. IEEE Transactions on Signal Processing 57(1), 289–301 (2009)

    Article  MathSciNet  Google Scholar 

  17. Duarte, L.T., Suyama, R., Attux, R., Romano, J.M.T., Jutten, C.: Blind extraction of sparse components based on ℓ0-norm minimization. In: Proc. of the IEEE Statistical Signal Processing Workshop, SSP (2011)

    Google Scholar 

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Fabian Theis Andrzej Cichocki Arie Yeredor Michael Zibulevsky

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© 2012 Springer-Verlag Berlin Heidelberg

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Duarte, L.T., Ando, R.A., Attux, R., Deville, Y., Jutten, C. (2012). Separation of Sparse Signals in Overdetermined Linear-Quadratic Mixtures. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_30

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  • DOI: https://doi.org/10.1007/978-3-642-28551-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28550-9

  • Online ISBN: 978-3-642-28551-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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