This paper presents a nonlinear mixing model for hyperspectral imageunmixing. The proposed model assumes that the pixel reflectances arepost-nonlinear functions of unknown pure spectral components contaminated by anadditive white Gaussian noise. These nonlinear functions are approximated usingpolynomials leading to a polynomial post-nonlinear mixing model. A Bayesianalgorithm is proposed to estimate the parameters involved in the model yieldingan unsupervised nonlinear unmixing algorithm. Due to the large number ofparameters to be estimated, an efficient Hamiltonian Monte Carlo algorithm isinvestigated. The classical leapfrog steps of this algorithm are modified tohandle the parameter constraints. The performance of the unmixing strategy,including convergence and parameter tuning, is first evaluated on syntheticdata. Simulations conducted with real data finally show the accuracy of theproposed unmixing strategy for the analysis of hyperspectral images.
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