Hyperspectral parameter estimation of elliptically contoured t mixture models using expectation‐maximisation

The remote sensing community has been interested in parameter estimation for many years, and with the maturation of hyperspectral imaging technology, it is natural to turn our attention to estimating parameters of models for hyperspectral data. Existing statistical models employ one or many normal distributions to account for spectral variability. However, recent work demonstrates the deviation from normality for many data, and the lack of robustness of normal models. As such, we develop adaptive probability density models for hyperspectral images based on a mixture of t distributions. Model parameters are estimated using the Expectation‐Maximization (EM) algorithm, both in a traditional and stochastic formulation, with t distributions to account for the long, heavy tails exhibited by remotely sensed hyperspectral data. What makes this paper unique is the fact that unlike earlier work that uses EM in the context of normal or other distributions, no manual manipulation is required during model generation, and all parameters (including the important degrees of freedom) are estimated simultaneously from the data. Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data demonstrate our automated approach, and clustering is performed based on posterior probabilities. Results are statistically evaluated for goodness‐of‐fit. While multivariate distributions are used to accommodate the vector nature of hyperspectral image pixels, the techniques developed here apply equally well to univariate distributions for standard image processing with scalar pixel values.