Markov random fields for joint unmixing and segmentation of hyperspectral images

This paper studies a new Bayesian algorithm for the unmixing of hyperspectral images. The proposed Bayesian algorithm is based on the well-known linear mixing model (LMM). Spatial correlations between pixels are introduced using hidden variables, or labels, and modeled via a Potts-Markov random field. We assume that the pure materials (or endmembers) contained in the image are known a priori or have been extracted by using an endmember extraction algorithm. The mixture coefficients (referred to as abundances) of the whole hyperspectral image are then estimated by using a hierarchical Bayesian algorithm. A reparametrization of the abundances is considered to handle the physical constraints associated to these parameters. Appropriate prior distributions are assigned to the other parameters and hyperparameters associated to the proposed model. To alleviate the complexity of the resulting joint distribution, a hybrid Gibbs algorithm is developed, allowing one to generate samples that are asymptotically distributed according to the full posterior distribution of interest. The generated samples are finally used to estimate the unknown model parameters. Simulations on synthetic data illustrate the performance of the proposed method.