Spectral Variability Aware Blind Hyperspectral Image Unmixing Based on Convex Geometry

Hyperspectral image unmixing has proven to be a useful technique to interpret hyperspectral data, and is a prolific research topic in the community. Most of the approaches used to perform linear unmixing are based on convex geometry concepts, because of the strong geometrical structure of the linear mixing model. However, many algorithms based on convex geometry are still used in spite of the underlying model not considering the intra-class variability of the materials. A natural question is to wonder to what extent these concepts and tools (Intrinsic Dimensionality estimation, endmember extraction algorithms, pixel purity) are still relevant when spectral variability comes into play. In this paper, we first analyze their robustness in a case where the linear mixing model holds in each pixel, but the endmembers vary in each pixel according to a prescribed variability model. In the light of this analysis, we propose an integrated unmixing chain which tries to adress the shortcomings of the classical tools used in the linear case, based on our previously proposed extended linear mixing model. We show the interest of the proposed approach on simulated and real datasets.