Modeling variability in hyperspectral imagery using a stochastic compositional approach

Hyperspectral data are typically analyzed using either a pure-pixel statistical classification approach based on a multivariate mixture distribution or a mixed-pixel linear or nonlinear deterministic model. We define a stochastic compositional model that synthesizes these two approaches: an observation is modeled as a constrained linear combination of random vectors. Parameters of the model are estimated using an iterative expectation-maximization maximum likelihood algorithm. The model may be used to estimate fractional abundances of the classes and to estimate the most likely contributor to each observation from each class. Anomaly and likelihood ratio detection algorithms are derived from the model. The linear mixture model and the stochastic compositional model are applied to simulated data and the abundance estimation error and anomaly detection performance are compared.