Characterization of the joint (among wavebands) probability density function (pdf) of hyperspectral imaging (HSI) data is crucial for several applications, including the design of constant false alarm rate (CFAR) detectors and statistical classifiers. HSI data are vector (or equivalently multivariate) data in a vector space with dimension equal to the number of spectral bands. As a result, the scalar statistics utilized by many detection and classification algorithms depend upon the joint pdf of the data and the vector-to-scalar mapping defining the specific algorithm. For reasons of analytical tractability, the multivariate Gaussian assumption has dominated the development and evaluation of algorithms for detection and classification in HSI data, although it is widely recognized that it does not always provide an accurate model for the data. The purpose ofthis paper is to provide a detailed investigation ofthejoint and marginal distributional properties of HSI data. To this end, we assess how well the multivariate Gaussian pdf describes HSI data using univariate techniques for evaluating marginal normality, and techniques that use unidimensional views (projections) of multivariate data. We show that the class of elliptically contoured distributions, which includes the multivariate normal distribution as a special case, provides a better characterization of the data. Finally, it is demonstrated that the class of univariate stable random variables provides a better model for the heavy-tailed output distribution of the well known matched filter target detection algorithm.

Date of creation, presentation, or exhibit



Proceedings of Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VII 4381 (2001) 308-316 "On the statistics of hyperspectral imaging data," Proceedings of Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VII. International Society of Optical Engineers. Held at AeroSpace in Orlando, Florida: 16-20 April 2001. Copyright 2001 Society of Photo-Optical Instrumentation Engineers. This paper was published in Proceedings of Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery VII, SPIE vol. 4381 and is made available as an electronic reprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. We wish to express our gratitude to CAPT Frank Garcia, DUSD (S&T), Program Manager HTAP, for his enthusiastic support. We also express our gratitude to SITAC for providing the calibrated and ground-truthed HYDICE data used in this work. This work was sponsored by the Department of the Defense Air Force contract F19628-95-C-0002. ISSN: 0277-786X Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Conference Proceeding

Department, Program, or Center

Chester F. Carlson Center for Imaging Science (COS)


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