New Bayesian approach for semi-supervised hyperspectral unmixing in linear mixing models

In this paper, a Bayesian framework algorithm is represented for hyperspectral image unmixing. The Additive Gaussian noise is considered in each hyperspectral pixel. We assume an extremely large spectral dictionary of endmembers is available. Whereas in practice each pixel could be presented by a small number of materials compared to the large number of endmembers of a spectral dictionary, the abundance vector would be a sparse vector. We propose the sparse Dirichlet prior for demonstrating the abundance vector. Thus, the proposed method could properly be used for semi-supervised unmixing problems wherein the exact existing endmembers in each pixel are unknown as well as the supervised problem. Because of complexity of the derived joint posterior of the abundances and noise variances, a Gibbs sampler is utilized to extract the abundance. Experimental results on simulated data demonstrate the capability of the proposed prior for accurate unmixing compared to the uniform distribution.