Spectral classification, segmentation and data reduction are the three main problems in hyperspectral image analysis. In this paper we propose a Bayesian estimation approach which tries to give a solution for these three problems jointly. The data reduction problem is modeled as a blind sources separation (BSS) where the data are the m hyperspectral images and the sources are the n < m images which must be mutually the most independent and piecewise homogeneous. To insure these properties, we propose a hierarchical model for the sources with a common hidden classification variable which is modelled via a Potts-Markov field. The joint Bayesian estimation of this hidden variable as well as the sources and the mixing matrix of the BSS problem gives a solution for all the three problems of spectra classification, segmentation and data reduction problems of hyperspectral images. An appropriate Gibbs Sampling (GS) algorithm is proposed for the Bayesian computationand a few simulation resu...