Application of Gibbs sampling in efficient hyperspectral unmixing based on the mixtures of Dirichlet components

Abstract

The independent component analysis has been commonly employed in hyperspectral unmixing. However, the success of this method is highly dependent on the independency of its sources assumption. Dependent component analysis (DECA) algorithm, which utilizes a Dirichlet mixture model, was developed to provide more adequate spectral unmixing of dependent sources. Estimation of the unknown model parameters using the expectation maximization algorithm in DECA resulted in some insufficiencies. DECAGibbs algorithm is introduced to improve unmixing accuracy by applying the Gibbs sampling method to the parameter estimation process of DECA, which is conducted in different manners of modeling the observations. Functionality of the DECAGibbs algorithm is examined through the artificial datasets and an AVIRIS image of Cuprite, Nevada, indicating better decomposition of mixed observations. Finally, the best performing model was employed in mineralogical mapping of the Lahroud region, northwest Iran, by a Hyperion image. The results represent the high reliability of the proposed method according to the geological studies of the area. Since the practical application of the mixture models relies upon the efficient estimation of their involved parameters, the performance of the DECA algorithm is improved by employing the Bayesian parameter estimation approaches in this research.