Previously, an analytical end-to-end spectral imaging system model has been developed. The model is constructed around the propagation of spectral statistics from the scene, through the sensor, and processing transformations to lead to prediction of a performance metric. In this analytical framework the description of the class statistics has been by their spectral mean vector and spectral covariance matrix (first and second order statistics). This representation is only strictly accurate when the underlying classes are Gaussian in nature. While some background classes fall into this category, many have been observed to be non-Gaussian in nature. As a work-around for this limitation, we have often formed sub-classes in the background, which when combined form a “composite” background class that can be multi-modal. However, we have observed in estimates of empirical data distributions that unimodal backgrounds often have longer tails than those predicted by the Gaussian distribution. Recently, it has been demonstrated that a family of distributions, known as the elliptically contoured multivariate t-distributions, can provide an accurate depiction of empirically observed backgrounds. These distributions are parameterized by their multivariate mean vector and covariance matrix, but also by a degree of freedom parameter, M. By varying M, excellent fits to empirical distributions have been observed. Another key feature of these distributions is that the number of degrees of freedom has been shown to be invariant to linear transformations. Since the analytical model operates by performing a sequence of linear transformations on the statistics, the input value of M is preserved and can be used at any stage of the model to represent the class statistics. This paper describes an implementation of the elliptically contoured t-distributions to represent background classes in the end-to-end system model. The functional form and examples of the t-distributions are shown. Results are presented comparing predictions of target detection performance using backgrounds modeled by multiclass Gaussian distributions with the new elliptical-t distributions.

Date of creation, presentation, or exhibit



Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (2004) 972-975 "Improved modeling of background distributions in an end-to-end spectral imaging system model," Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS). Institute of Electrical and Electronics Engineers (IEEE). Held in Anchorage, Alaska: 20-24 September 2004. ©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. This work was performed while Dr. Kerekes was at MIT Lincoln Laboratory. ISBN: 0-7803-8742-2Note: 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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