Application of stochastic mixing models to hyperspectral detection problems

Hyperspectral images are frequently analyzed in terms of the linear mixing model, which assumes that observed pixel radiances are generated by linear combinations of a relatively small number of spectral constituent signatures. The constituents are generally modeled as deterministic points in color space whose locations can in principle be found by exploiting the convex geometry of the mixture simplex. This paper presents an alternative stochastic mixing model (SMM) that associates scene constituents with distinct probability distributions,the parameters of which are estimated from observed data using statistical clustering methods. By defining distributions corresponding to both constituent and mixed pixel classes, the SMM can often be used to generate physically meaningful classification maps of spectrally-heterogeneous scenes. However, the most significant application of the stochastic approach is to hyperspectral target detection based on statistical decision theory concepts. A SMM can provide accurate parametric estimates of the spectral distributions for mixed scenes, thereby improving the performance of hypothesis testing procedures that utilize replacement targets with spectral signature uncertainty. SMM principles and applications are illustrated using hyperspectral imagery collected by the LIFTIRS and HYDICE instruments.