Abstract
In this paper, a blind source separation method for bilinear mixtures of two source signals is presented, that relies on nonlinear correlation between separating system outputs. An estimate of each source is created by linearly combining observed mixtures and maximizing a cost function based on the correlation between the element-wise product of the estimated sources and the corresponding quadratic term. A proof of the method separability, i.e. of the uniqueness of the solution to the cost function maximization problem, is also given. The algorithm used in this work is also presented. Its effectiveness is demonstrated through tests with artificial mixtures created with real Earth observation spectra. The proposed method is shown to yield much better performance than a state-of-the-art method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Meganem, I., Déliot, P., Briottet, X., Deville, Y., Hosseini, S.: Linear-quadratic mixing model for reflectances in urban environments. IEEE Trans. Geosci. Remote Sens. 52, 544–558 (2014)
Meganem, I., Deville, Y., Hosseini, S., Déliot, P., Briottet, X.: Linear-quadratic blind source separation using NMF to unmix urban hyperspectral images. IEEE Trans. Sign. Process. 62, 1822–1833 (2014)
Duarte, L.T., Jutten, C., Moussaoui, S.: Bayesian source separation of linear and linear-quadratic mixtures using truncated priors. J. Sign. Process. Syst. 65, 311–323 (2011)
Deville, Y.: Matrix factorization for bilinear blind source separation: methods, separability and conditioning. In: Proceedings of the 23rd European Signal Processing Conference, Nice, France, pp. 1945–1949 (2015)
Cardoso, J.F.: The three easy routes to independent component analysis, contrasts and geometry. In: Proceedings of the ICA 2001 workshop, San Diego, pp. 1–6 (2001)
Gribonval, R., Lesage, S.: A survey of sparse component analysis for blind source separation: principles, perspectives, and new challenges. In: Proceedings of the 14th European Symposium on Artificial Neural Networks, Bruges, Belgium, pp. 323–330 (2006)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Neural Information Processing Systems, pp. 556–562 (2001)
Ando, R.A., Jutten, C., Rivet, B., Attux R., Duarte, L.T.: Nonlinear blind source separation for chemical sensor arrays based on a polynomial representation. In: 24th European Signal Processing Conference (EUSIPCO), pp. 2146–2150 (2016)
Comon, P., Jutten, C.: Handbook of Blind Source Separation. Independent Component Analysis and Applications. Academic Press, Oxford (2010)
Theodoridis, S., Koutroumbas, K.: Pattern Recognition. Academic Press, Oxford (2009)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001)
Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.I.: Nonnegative matrix and tensor factorizations. Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, Chichester (2009)
Makino, S., Lee, T.W., Sawada, H.: Blind speech separation. Springer, Dordrecht (2007)
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, Cham (2015). https://doi.org/10.1007/978-3-319-22482-4_18
Deville, Y.: Blind source separation and blind mixture identification methods. In: Wiley Encyclopedia of Electrical and Electronics Engineering. pp. 1–33 (2016). J. Webster
Kokaly, R.F., Clark, R.N., Swayze, G.A., Livo, K.E., Hoefen, T.M., Pearson, N.C., Wise, R.A., Benzel, W.M., Lowers, H.A., Driscoll, R.L., Klein, A.J.: USGS Spectral Library Version 7: U.S. Geological Survey Data Series 1035 (2017). https://doi.org/10.3133/ds1035
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Guerrero, A., Deville, Y., Hosseini, S. (2018). A Blind Source Separation Method Based on Output Nonlinear Correlation for Bilinear Mixtures. In: Deville, Y., Gannot, S., Mason, R., Plumbley, M., Ward, D. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2018. Lecture Notes in Computer Science(), vol 10891. Springer, Cham. https://doi.org/10.1007/978-3-319-93764-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-93764-9_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93763-2
Online ISBN: 978-3-319-93764-9
eBook Packages: Computer ScienceComputer Science (R0)