Efficient Use of Endmember Variability for Spectral Unmixing

Abstract

Spectral data from the biological and environmental sciences often consist of a mixed signal vector, which is composed of a weighted sum of random, unobserved endmember vectors. Such a mixed signal has a mean and a variance that both depend on the unknown weights, which represent the contribution of each endmember to the total signal. Linear estimates of the weights based on the mean model are often used, but these are likely to be inefficient, and could be improved upon by estimates that also make use of the variance model. In the context of a latent factor model for source variability, we calculate theoretically how much information is available in the variance model, and demonstrate how this information may stabilize inference in the case of an ill-conditioned mean model. We further propose nonlinear estimators that make use of the variance model information. We show using data collected in water quality monitoring, bacterial imaging, and remote sensing contexts that utilization of the variance model improves estimation of the mixing weights.