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Estimation of elliptically contoured mixture models for hyperspectral imaging data

Gaussian mixture modeling (GMM) has become a popular method for representing the statistical variability of spectrally inhomogeneous hyperspectral imaging (HSI) data. Finite mixture models can be applied to image segmentation, which can be considered a sort of blind classification, which is useful when there is no a priori information available about the materials in the scene. However, the GMM approach can be insufficient for many HSI data sets since the Gaussian has fixed narrow tails, uncharacteristic of operational HSI data. Elliptically contoured distributions (ECDs), specifically the multivariate t, have been shown to better fit HSI data. In this paper we develop mixtures of ECDs for the task of robustly modeling hyperspectral image data. An approach based on the EM algorithm is developed for concurrently estimating all parameters in a t mixture, assuming nothing but that the number of components are known. Results from the automatic segmentation of AVIRIS data illustrate the utility of t mixture models using this EM approach for parameter estimation.