Library-based linear unmixing for hyperspectral imagery via reversible jump MCMC sampling

This paper studies a semi-supervised algorithm for linear hyperspectral unmixing. The proposed unmixing method assumes that the pure material spectra denoted as endmembers belong to a library that is a priori available. However, the number and the nature of endmembers appearing in the pixel are not known a priori, resulting in a model selection problem. This paper proposes to handle this model selection problem within a fully Bayesian framework. First, appropriate distributions are elected as prior distributions for the unknown parameters. Particularly, a distribution defined on a simplex is chosen as prior for an appropriate partial abundance vector to ensure the positivity and the sum-to-one constraints of the mixing coefficients. Due to the complexity of the posterior distribution, a reversible jump Markov chain Monte Carlo algorithm is proposed to estimate the number and the nature of the macroscopic materials, as well as their respective proportions in the pixel. The accuracy of the proposed method is illustrated by simulations on synthetic hyperspectral data.