A reversible-jump mcmc algorithm for estimating the number of endmembers in the normal compositional model application to the unmixing of hyperspectral images

In this paper, we address the problem of unmixing hyperspectral images in a semi-supervised framework using the normal compositional model recently introduced by Eismann and Stein. Each pixel of the image is modeled as a linear combination of random endmembers. More precisely, endmembers are modeled as Gaussian vectors whose means belong to a known spectral library. This paper proposes to estimate the number of endmembers involved in the mixture, as well as the mixture coefficients (referred to as abundances) using a trans-dimensional algorithm. Appropriate prior distributions are assigned to the abundance vector (to satisfy constraints inherent to hyperspectral imagery), the noise variance and the number of components involved in the mixture model. The computational complexity of the resulting posterior distribution is alleviated by constructing an hybrid Gibbs algorithm which generates samples distributed according to this posterior distribution. As the number of endmembers is unknown, the sampler has to jump between spaces of different dimensions. This is achieved by a reversible jump Markov chain Monte Carlo method that allows one to handle the model order selection problem. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic data.