Bayesian Approach With Hidden Markov Modeling and Mean Field Approximation for Hyperspectral Data Analysis

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.