Application of multivariate Gaussian detection theory to known non-Gaussian probability density functions

Craig R. Schwartz; Brian J. Thelen; Arthur C. Kenton

doi:10.1117/12.211374

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20 June 1995 Application of multivariate Gaussian detection theory to known non-Gaussian probability density functions

Craig R. Schwartz, Brian J. Thelen, Arthur C. Kenton

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Proceedings Volume 2496, Detection Technologies for Mines and Minelike Targets; (1995) https://doi.org/10.1117/12.211374
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

A statistical parametric multispectral sensor performance model was developed by ERIM to support mine field detection studies, multispectral sensor design/performance trade-off studies, and target detection algorithm development. The model assumes target detection algorithms and their performance models which are based on data assumed to obey multivariate Gaussian probability distribution functions (PDFs). The applicability of these algorithms and performance models can be generalized to data having non-Gaussian PDFs through the use of transforms which convert non-Gaussian data to Gaussian (or near-Gaussian) data. An example of one such transform is the Box-Cox power law transform. In practice, such a transform can be applied to non-Gaussian data prior to the introduction of a detection algorithm that is formally based on the assumption of multivariate Gaussian data. This paper presents an extension of these techniques to the case where the joint multivariate probability density function of the non-Gaussian input data is known, and where the joint estimate of the multivariate Gaussian statistics, under the Box-Cox transform, is desired. The jointly estimated multivariate Gaussian statistics can then be used to predict the performance of a target detection algorithm which has an associated Gaussian performance model.

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Craig R. Schwartz, Brian J. Thelen, and Arthur C. Kenton "Application of multivariate Gaussian detection theory to known non-Gaussian probability density functions", Proc. SPIE 2496, Detection Technologies for Mines and Minelike Targets, (20 June 1995); https://doi.org/10.1117/12.211374

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