Extended-Linear Hyperspectral Mixing Models

A mixture model for hyperspectral data describes the underlying physics of how constituent substances in a scene affect each other to produce radiance received at each detector pixel. In the linear models the total scene is portrayed as a checkerboard mixture of reflecting surfaces containing fractional abundances of the constituent substances. The radiance measured at a detector pixel is modeled proportional to the same abundance of the constituents where interference (interaction) between constituent substances is neglected. In this paper we present a model to account for a multiple reflection process whereby the measured radiation is the result of multiple inelastic interactions (scattering or reflection) among the constituent components in the scene. While this process is inherently non-linear, and we have constructed an equivalent "extended" linear version of the model, which yields the effective abundance of the end members in the scene. This model seamlessly reduces to the conventional linear model when multiple scattering is absent. We present results of preliminary applications of these models with standard unmixing algorithm. The results show that the inclusion of higher order reflections always produces progressively a better description of the abundances and the interactions between the endmembers in the scene.