24 October 2012 A unified theory for target-specified virtual dimensionality of hyperspectral imagery
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Virtual dimensionality (VD) is defined as the number of spectrally distinct signatures in hyperspectral data. Unfortunately, there is no provided specific definition of what “spectrally distinct signatures” are. As a result, many techniques developed to estimate VD have produced various values for VD. This paper develops a unified theory for VD of hyperspectral imagery where the value of VD is completely determined by the targets of interest characterized by their spectral statistics. Using this new developed theory the VD techniques can be categorized according to targets characterized by various orders of statistics into 1st order statistics-based, 2nd order of statistics-based and high order statistics (HOS)-based methods. In order to determine the number of specific targets of interest, a binary composite hypothesis testing problem is formulated where a target of interest is considered as a desired signal under the alternative hypothesis while the null hypothesis represents absence of the target. With this interpretation many VD estimation techniques can be unified under the same framework, for example, Harsanyi-Farrand-Chang (HFC) method, maximum orthogonal complement algorithm (MOCA).
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Chein-I Chang, Chein-I Chang, } "A unified theory for target-specified virtual dimensionality of hyperspectral imagery", Proc. SPIE 8539, High-Performance Computing in Remote Sensing II, 85390J (24 October 2012); doi: 10.1117/12.979189; https://doi.org/10.1117/12.979189

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