On the modeling of hyperspectral imaging data with elliptically contoured distributions

Accurate statistical models for hyperspectral imaging (HSI) data are fundamental for many subsequent applications including detection, classification, and estimation. Suppose the whole nonhomogeneous HSI data is well classified into homogeneous unimodal clutters, we find that the family of elliptically contoured distributions (ECDs) is capable of providing sufficiently accurate model for each clutter. In this paper, several techniques are applied to test the elliptical symmetry of HSI clutters. Instead of testing elliptical symmetry directly, its counterpart spherical symmetry is examined for the whitened unimodal clutters. For each clutter which passes these symmetry checking tests, fitting an appropriate ECD based model to the data can be done in the Mahalanobis distance direction.