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. © 2012 Springer-Verlag.7191 LNCS 239246Yitzhak Chaya Weinstein Res. Inst. Signal Process.,Tel-Aviv University,The Technion - Israel Institute of Technology,Bar-Ilan University,The Advanced Communication CenterComon, P., Jutten, C., (2010) Handbook of Blind Source Separation, Independent Component Analysis and Applications, , Academic Press, ElsevierRomano, J.M.T., Attux, R.R.F., Cavalcante, C.C., Suyama, R., (2011) Unsupervised Signal Processing: Channel Equalization and Source Separation, , CRC PressDuarte, L.T., Jutten, C., Moussaoui, S., A Bayesian nonlinear source separation method for smart ion-selective electrode arrays (2009) IEEE Sensors Journal, 9 (12), pp. 1763-1771Meganem, I., Deville, Y., Hosseini, S., Déliot, P., Briottet, X., Duarte, L.T., Linear-quadratic and polynomial non-negative matrix factorizationapplication to spectral unmixing (2011) Proc. of the 19th European Signal Processing Conference, EUSIPCO 2011Jutten, C., Karhunen, J., Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures (2004) International Journal of Neural Systems, 14, pp. 267-292Comon, P., Independent component analysis, a new concept? (1994) Signal Processing, 36, pp. 287-314Hosseini, S., Deville, Y., Blind Separation of Linear-Quadratic Mixtures of Real Sources Using a Recurrent Structure (2003) LNCS, 2687, pp. 241-248. , Mira, J., Álvarez, J.R. (eds.) IWANN 2003. Springer, HeidelbergMerrikh-Bayat, F., Babaie-Zadeh, M., Jutten, C., Linear-quadratic blind source separating structure for removing show-through in scanned documents (2010) International Journal on Document Analysis and Recognition, pp. 1-15Bedoya, G., (2006) Nonlinear Blind Signal Separation for Chemical Solid-state Sensor Arrays, , PhD thesis, Universitat Politecnica de CatalunyaDeville, Y., Hosseini, S., Recurrent networks for separating extractable-target non-linear mixtures. part i: Non-blind configurations (2009) Signal Processing, 89, pp. 378-393Castella, M., Inversion of polynomial systems and separation of nonlinear mixtures of finite-alphabet sources (2008) IEEE Trans. on Sig. Proc., 56 (8), pp. 3905-3917Abed-Meraim, K., Belouchrani, A., Hua, Y., Blind identification of a linear-quadratic mixture of independent components based on joint diagonalization procedure Proc. of the IEEE Inter. Conf. on Acous., Spee., and Signal Processing, ICASSP (1996)Deville, Y., Hosseini, S., Blind identification and separation methods for linear-quadratic mixtures and/or linearly independent non-stationary signals Proc. of the 9th Int. Symp. on Sig. Proc. and Its App., ISSPA (2007)Duarte, L.T., Suyama, R., Attux, R., Deville, Y., Romano, J.M.T., Jutten, C., Blind Source Separation of Overdetermined Linear-Quadratic Mixtures (2010) LNCS, 6365, pp. 263-270. , Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds.) LVA/ICA 2010. Springer, HeidelbergElad, M., (2010) Sparse and Redundant Representations from Theory to Applications in Signal and Image Processing, , Springer, HeidelbergMohimani, H., Babaie-Zadeh, M., Jutten, C., A fast approach for overcomplete sparse decomposition based on smoothed ℓ 0 norm (2009) IEEE Transactions on Signal Processing, 57 (1), pp. 289-301Duarte, L.T., Suyama, R., Attux, R., Romano, J.M.T., Jutten, C., Blind extraction of sparse components based on ℓ 0-norm minimization Proc. of the IEEE Statistical Signal Processing Workshop, SSP (2011)