Anomaly detection based on the statistics of hyperspectral imagery

The purpose of this paper is to introduce a new anomaly detection algorithm for application to hyperspectral imaging (HSI) data. The algorithm uses characterisations of the joint (among wavebands) probability density function (pdf) of HSI data. Traditionally, the pdf has been assumed to be multivariate Gaussian or a mixture of multivariate Gaussians. Other distributions have been considered by previous authors, in particular Elliptically Contoured Distributions (ECDs). In this paper we focus on another distribution, which has only recently been defined and studied. This distribution has a more flexible and extensive set of parameters than the multivariate Gaussian does, yet the pdf takes on a relatively simple mathematical form. The result of all this is a model for the pdf of a hyperspectral image, consisting of a mixture of these distributions. Once a model for the pdf of a hyperspectral image has been obtained, it can be incorporated into an anomaly detector. The new anomaly detector is implemented and applied to some medium wave infra-red (MWIR) hyperspectral imagery. Comparison is made with a well-known anomaly detector, and it will be seen that the results are promising.