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12 August 2004 Using elliptically contoured distributions to model hyperspectral imaging data and generate statistically similar synthetic data
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Developing proper models for Hyperspectral imaging (HSI) data allows for useful and reliable algorithms for data exploitation. These models provide the foundation for development and evaluation of detection, classification, clustering, and estimation algorithms. To date, most algorithms have modeled real data as multivariate normal, however it is well known that real data often exhibits non-normal behavior. In this paper, Elliptically Contoured Distributions (ECDs) are used to model the statistical variability of HSI data. Non-homogeneous data sets can be modeled as a finite mixture of more than one ECD, with different means and parameters for each component. A larger family of distributions, the family of ECDs includes the multivariate normal distribution and exhibits most of its properties. ECDs are uniquely defined by their multivariate mean, covariance and the distribution of its Mahalanobis distance metric. This metric lets multivariate data be identified using a univariate statistic and can be adjusted to more closely match the longer tailed distributions of real data. One ECD member of focus is the multivariate t-distribution, which provides longer tailed distributions than the normal, and has an F-distributed Mahalanobis distance statistic. This work will focus on modeling these univariate statistics, using the Exceedance metric, a quantitative goodness-of-fit metric developed specifically to improve the accuracy of the model to match the long probabilistic tails of the data. This metric will be shown to be effective in modeling the univariate Mahalanobis distance distributions of hyperspectral data from the HYDICE sensor as either an F-distribution or as a weighted mixture of F-distributions. This implies that hyperspectral data has a multivariate t-distribution. Proper modeling of Hyperspectral data leads to the ability to generate synthetic data with the same statistical distribution as real world data.
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David B. Marden and Dimitris G. Manolakis "Using elliptically contoured distributions to model hyperspectral imaging data and generate statistically similar synthetic data", Proc. SPIE 5425, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery X, (12 August 2004);

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