A Probabilistic Approach to Spectral Unmixing

Abstract

In this paper, we present a statistical approach to spectral unmixing with unknown endmember spectra and unknown illuminant power spectrum. The method presented here is quite general in nature, being applicable to settings in which sub-pixel information is required. The method is formulated as a simultaneous process of illuminant power spectrum prediction and basis material reflectance decomposition via a statistical approach based upon deterministic annealing and the maximum entropy principle. As a result, the method presented here is related to soft clustering tasks with a strategy for avoiding local minima. Furthermore, the final endmembers depend on the similarity between pixel reflectance spectra. Hence, the method does not require a preset number of material clusters or spectral signatures as input. We show the utility of our method on trichromatic and hyperspectral imagery and compare our results to those yielded by alternatives elsewhere in the literature.