Accuracy and performance of optimized Bayesian Source Separation for hyperspectral unmixing

Bayesian Source Separation (BPSS) with non-negativity constraints is a useful unsupervised approach for hyperspectral data unmixing. The main goal of this approach is to ensure the non-negativity of the unmixed source spectra as well as of the abundances. Moreover, a recent extension has been proposed to impose the sum-to-one (full additivity) constraint on the estimated source abundances of each pixel. Unfortunately, even though non-negativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms is limited by high computation time and large memory requirements since these Bayesian algorithms employ Markov Chain Monte Carlo methods. This article describes an implementation strategy which allow to apply such algorithms on a full hyperspectral image, of typical size in Earth and Planetary Sciences, with reasonable computational cost. In this paper, not only optimizations on the technical level are proposed but we also study the effect of convex hull pixel selection as a preprocessing and sampling step and discuss the impact of such preprocessing on the relevance of the estimated component spectra and abundance maps, as well as on the whole computation times. For that purpose, two different datasets are employed: a synthetic one and a real hyperspectral image from Mars.