Unmixing using a combined microscopic and macroscopic mixture model with distinct endmembers

Much work in the study of hyperspectral imagery has focused on macroscopic mixtures and unmixing via the linear mixing model. A substantially different approach seeks to model hyperspectral data non-linearly in order to accurately describe intimate or microscopic relationships of materials within the image. In this paper we present and discuss a new model (MacMicDEM) that seeks to unify both approaches by representing a pixel as both linearly and non-linearly mixed, with the condition that the endmembers for both mixture types need not be related. Using this model, we develop a method to accurately and quickly unmix data which is both macroscopically and microscopically mixed. Subsequently, this method is then validated on synthetic and real datasets.