A Novel Spectral Unmixing Method Incorporating Spectral Variability Within Endmember Classes

Some spectral unmixing methods incorporate end-member variability within endmember classes. It is, however, uncertain whether these methods work well when endmember spectra do not completely describe the variability that exists within endmember classes. This paper proposes a novel spectral unmixing method, Spectral Unmixing within a multi-task Gaussian Process framework (SUGP), which is more resistant to problems caused by the use of a small number of endmember spectra. SUGP models the latent function between spectra and abundances in a training set and predicts abundances from a given pixel spectrum. SUGP is different from existing methods in that it incorporates all spectra within each endmember class to estimate abundances within a probabilistic framework. Using simulated data, SUGP was compared with existing linear unmixing methods and was found to be superior in determining the number of endmember classes within each pixel and in estimating abundances. It was also more effective in cases where a small number of spectra within endmember classes were specified and was more resistant to the effects of spectral noise. Methods were applied to the hyperspectral imagery of a mine wall and to imagery acquired over Cuprite, Nevada. Abundance maps generated by SUGP were consistent with the validated reference maps. SUGP opens up possibilities for estimating accurate abundances under conditions where endmember variability is present and where endmember spectra incompletely describe the true variability of each endmember class.