Linear-quadratic And Polynomial Non-negative Matrix Factorization; Application To Spectral Unmixing

In this article, we present a source separation method for linear-quadratic models. This class of mixing models is encountered in various real applications, such as hyperspectral unmixing for urban environments. Linear-quadratic mixing models are less studied in the literature than linear ones but there exist some methods for handling them, essentially Bayesian or based on Independent Component Analysis. We propose a separation method based on Non-negative Matrix Factorization (NMF). This class of methods is well-suited for many applications where data is positive and satisfies a linear model. The originality of our work is that we here developed an extension of NMF suited to linear-quadratic models. We also show how we can extend this method to the more general case of polynomial models. Our method for linear-quadratic models is tested with mixtures of artificial signals and yields attractive performance. We also apply it to hyperspectral unmixing, by testing it with artificial mixtures of reflectance spectra, which gives encouraging results. © 2011 EURASIP.18591863Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.-I., (2009) Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation, , John Wiley and SonsHosseini, S., Deville, Y., Blind maximum likelihood separation of a linear-quadratic mixture (2004) Rftxt Proceedings of the Fifth International Conference on Independent Component Analysis and Blind Signal Separation (ICA), , Granada, Spain, Erratum: http://arxiv.org/abs/1001.0863Duarte, L.T., Jutten, C., Moussaoui, S., Bayesian source separation of linear-quadratic and linear mixtures through a MCMC method (2009) Proceedings of IEEE MLSP, , Grenoble, France, Sept. 2-4Mokhtari, F., Babaie-Zadeh, M., Jutten, C., Blind separation of bilinear mixtures using mutual information minimization (2009) Proceedings of IEEEMLSP, Grenoble, France, , Sept. 2-4Moussaoui, S., Brie, D., Idier, J., Non-negative source separation: Range of admissible solutions and conditions for the uniqueness of the solution (2005) Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 5, pp. 289-292Somers, B., Cools, K., Delalieux, S., Stuckens, J., Zande Der D.Van, Verstraeten, W.W., Coppin, P., (2009) Nonlinear Hyperspectral Mixture Analysis for Tree Cover Estimates in Orchards, 113 (6), pp. 1183-1193. , Remote Sensing of EnvironmentNascimento, J.M.P., Bioucas-Dias, J.M., (2009) Nonlinear Mixture Model for Hyperspectral Unmixing, , SPIE Conference on Image and Signal Processing for Remote Sensing XVPetersen, K.B., Pedersen, M.S., (2008) The Matrix Cookbook, , http://matrixcookbook.com/, Technical University of Denmar

Non-linear unmixing of hyperspectral images using multiple-kernel self-organizing maps

International audienceThe spatial pixel resolution of common multispectral and hyperspectral sensors is generally not sufficient to avoid thatmultiple elementary materials contribute to the observed spectrum of a single pixel. To alleviate this limitation, spectral unmixingis a by-pass procedure which consists in decomposing the observed spectra associated with these mixed pixels into a set ofcomponent spectra, or endmembers, and a set of corresponding proportions, or abundances, that represent the proportion ofeach endmember in these pixels. In this study, a spectral unmixing technique is proposed to handle the challenging scenario of non-linear mixtures. This algorithm relies on a dedicated implementation of multiple-kernel learning using self-organising mapproposed as a solver for the non-linear unmixing problem. Based on a priori knowledge of the endmember spectra, it aims atestimating their relative abundances without specifying the non-linear model under consideration. It is compared to state-of-the-art algorithms using synthetic yet realistic and real hyperspectral images. Results obtained from experiments conducted onsynthetic and real hyperspectral images assess the potential and the effectiveness of this unmixing strategy. Finally, therelevance and potential parallel implementation of the proposed method is demonstrated