An information-theoretic approach to spectral variability, similarity, and discrimination for hyperspectral image analysis

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Abstract
A hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths. As a result, a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability, similarity and discrimination. In this correspondence, we present a new hyperspectral measure, Spectral Information Measure (SIM), to describe spectral variability and two criteria, spectral information divergence and spectral discriminatory probability, for spectral similarity and discrimination, respectively. The spectral information measure is an information-theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution. Spectral Information Divergence (SID) compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures. The spectral discriminatory probability calculates spectral probabilities of a spectral database (library) relative to a pixel to be identified so as to achieve material identification. In order to compare the discriminately power of one spectral measure relative to another, a criterion is also introduced for performance evaluation, which is based on the power of discriminating one pixel from another relative to a reference pixel. The experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used Spectral Angle Mapper (SAM).