Distance metrics and band selection in hyperspectral processing with applications to material identification and spectral libraries

At the core of most hyperspectral processing algorithms are distance metrics that compare two spectra and return a scalar value based on some notion of similarity. The two most common distance metrics in hyperspectral processing are the spectral angle mapper (SAM) and the Euclidean minimum distance (EMD), and each metric possesses distinct mathematical and physical properties. In this paper, we enumerate the characteristics of both metrics, and, based on an exact decomposition of SAM, we derive a technique called band add-on (BAO) that iteratively selects bands to increase the angular separation between two spectra. Unlike other feature selection algorithms, BAO exploits a mathematical decomposition of SAM to incrementally add bands. We extend BAO to the more practical problem of increasing the angular separability between two classes of spectra. This scenario parallels the material identification problem where quite often only a small number (<10) of ground-truth measurements are collected for each material class, and statistical classification methods are inapplicable. Two algorithms for selecting bands and class templates are presented to increase the angular separation between two classes. The techniques are compared with several other metric-based approaches in binary discrimination tests with real data. The results demonstrate that band selection can improve the discrimination of very similar targets, while using only a fraction of the available spectral bands.