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Effects of dimensionality reduction on the statististical distribution of hyperspectral backgrounds

The objective of this paper is to investigate the effects of dimensionality reduction on the statistical distribution of natural hyperspectral backgrounds. The statistical modeling is based on application of the multivariate t-elliptically contoured distribution to background regions which have been shown to exhibit "long-tail" behavior. Hyperspectral backgrounds are commonly represented with reduced dimensionality in order to minimize statistical redundancies in the spectral dimension and to satisfy data processing and storage requirements. In this investigation, we extend the statistical characterization of these backgrounds by modeling their Mahalanobis distance distributions in reduced dimensional space. The dimensionality reduction techniques applied in this paper include Principal Components Analysis (PCA) and spectral band aggregation. The knowledge gained from a better understanding of the effects of dimensionality reduction will be beneficial toward improving threshold selection for target detection applications. These investigations are done using hyperspectral data from the AVIRIS sensor and include spectrally homogeneous regions of interest obtained by visual interactive spatial segmentation.