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Physical modelling and non-linear unmixing method for urban hyperspectral images

Hyperspectral unmixing consists in decomposing pixel spectra into constituent spectra corresponding to pure materials (endmembers). Most existing methods are based on linear mixtures of the reflectance endmembers, which is only valid when the surface is flat and homogeneous. In the case of urban area sensing, due to the 3D structure of the buildings, such assumptions are no more valid. In this paper, we first derive the mixing model faced in urban spectral unmixing. Starting from physical equations based on radiative transfer theory, we deduce a linear-quadratic model. Then, a suitable unmixing method is proposed to extract the spectra of the materials composing the pixels. Our study led us to an original use of NMF (Non-negative Matrix Factorization) methods. The proposed algorithm is tested with synthetic mixtures of real endmember spectra, corresponding to cases with simple geometrical shapes that can be encountered in urban areas. First results are encouraging and show good agreement with respect to spectral signature.