Fast Hyperspectral Feature Reduction Using Piecewise Constant Function Approximations

The high number of spectral bands that are obtained from hyperspectral sensors, combined with the often limited ground truth, solicits some kind of feature reduction when attempting supervised classification. This letter demonstrates that an optimal constant function representation of hyperspectral signature curves in the mean square sense is capable of representing the data sufficiently to outperform, or match, other feature reduction methods such as principal components transform, sequential forward selection, and decision boundary feature extraction for classification purposes on all of the four hyperspectral data sets that we have tested. The simple averaging of spectral bands makes the resulting features directly interpretable in a physical sense. Using an efficient dynamic programming algorithm, the proposed method can be considered fast.