This paper addresses the problem of hyperspectral image unmixing. A new hierarchical Bayesian algorithm is proposed to estimate the coefficients of a linear mixture of spectra associated to a given pixel of the image. Appropriate priors are introduced to guaranty the positivity and additivity constraints inherent to the mixture coefficients. These coefficients referred to as abundances are then estimated from their posterior following the principles of Bayesian inference. The estimation is performed by using a Gibbs sampling strategy which generates samples distributed according the abundance posterior distribution. These samples are then averaged yielding the abundance minimum mean square error estimator
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