Supervised planetary unmixing with optimal transport

This paper is focused on spectral unmixing and present an original technique based on Optimal Transport. Optimal Transport consists in estimating a plan that transports a spectrum onto another with minimal cost, enabling to compute an associated distance (Wasserstein distance) that can be used as an alternative metric to compare hyperspectral data. This is exploited for spectral unmixing where abundances in each pixel are estimated on the basis of their projections in a Wasserstein sense (Bregman projections) onto known endmembers. In this work an over-complete dictionary is used to deal with internal variability between endmembers, while a regularization term, also based on Wasserstein distance, is used to promote prior proportion knowledge in the endmember groups. Experiments are performed on real hyperspectral data of asteroid 4-Vesta.