The main problems in hyperspectral image analysis are spectral classification, segmentation, and data reduction. In this paper, we propose a Bayesian estimation approach which gives a joint solution for these problems. The problem is modeled as a blind sources separation (BSS). The data are M hyperspectral images and the sources are K < M images which are composed of compact homogeneous regions and have mutually disjoint supports. The set of all these regions cover the total surface of the observed scene. To insure these properties, we propose a hierarchical Markov model for the sources with a common hidden classification field which is modeled via a Potts-Markov field. The joint Bayesian estimation of the hidden variable, sources, and the mixing matrix of the BSS gives a solution for all three problems: spectra classification, segmentation, and data reduction of hyperspectral images. The mean field approximation (MFA) algorithm for the posterior laws is proposed for the effective Bayesian computation. Finally, some results of the application of the proposed methods on simulated and real data are given to illustrate the performance of the proposed method compared to other classical methods, such as PCA and ICA.

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Hyperspectral images can be represented either as a set of images or as a set of spectra. Spectral classification and segmentation and data reduction are the main problems in hyperspectral image analysis. In this paper we propose a Bayesian estimation approach with an appropriate hiearchical model with hidden markovian variables which gives the possibility to jointly do data reduction, spectral classification and image segmentation. In the proposed model, the desired independent components are piecewise homogeneous images which share the same common hidden segmentation variable. Thus, the joint Bayesian estimation of this hidden variable as well as the sources and the mixing matrix of the source separation problem gives a solution for all the three problems of dimensionality reduction, spectra classification and segmentation of hyperspectral images. A few simulation results illustrate the performances of the proposed method compared to other classical methods usually used in hyperspectral image processing.

Dimensionality reduction, spectral classification and segmentation are the three main problems in hyperspectral image analysis. In this paper we propose a Bayesian estimation approach which gives a solution for these three problems jointly. The data reduction problem is modeled as a blind sources separation (BSS) where the sources are the images which must be mutually 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 as 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 dimensionality reduction, spectra classification and segmentation of hyperspectral images. For the Bayesian computation, we propose to use either Gibbs Sampling (GS) or Mean Field Approximation (MFA) methods. A few simulation results illustrate the performances of the proposed method and some comparison with other classical methods of PCA and ICA used for BSS.