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.
Chapter PDF
Similar content being viewed by others
References
Taleb, A., Jutten, C.: Source separation in post-nonlinear mixtures. IEEE Trans. on Signal Processing 47(10), 2807–2820 (1999)
Jutten, C., Babaie-Zadeh, M., Hosseini, S.: Three easy ways for separating nonlinear mixtures? Signal Processing 84(2), 217–229 (2004)
Almeida, L.B.: MISEP - linear and nonlinear ICA based on mutual information. Journal of Machine Learning Research 4, 1297–1318 (2003)
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)
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)
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
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)
Taleb, A.: A generic framework for blind source separation in structured nonlinear models. IEEE Trans. Sig. Proc. 50(8), 1819–1830 (2002)
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)
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)
Nocedal, J., Wright, S.: Numerical optimization. Springer (2006)
Bishop, C.M.: Neural networks for pattern recognition, Oxford (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hosseini, S., Deville, Y., El Amine, S., Saylani, H. (2012). Nonlinear Blind Source Separation Applied to a Simple Bijective Model. In: Elmoataz, A., Mammass, D., Lezoray, O., Nouboud, F., Aboutajdine, D. (eds) Image and Signal Processing. ICISP 2012. Lecture Notes in Computer Science, vol 7340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31254-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-31254-0_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31253-3
Online ISBN: 978-3-642-31254-0
eBook Packages: Computer ScienceComputer Science (R0)