Rational function approximation for feature reduction in hyperspectral data

In this letter, we propose a feature extracting technique by using rational function curve fitting. A unique rational function curve is developed to fit the spectral signature of each pixel in a hyperspectral image. Polynomial coefficients in the numerator and denominator of the fitted curve are considered as new extracted features. The main contribution of this letter is utilization of curve-fitting ability in order to classify and compress hyperspectral data. In other words, naturally different curves can be discriminated when they are approximated by rational functions with equal form, but different amounts of coefficients. This rational function curve fitting feature extraction method provides better classification results compared to some common feature extraction algorithms when a maximum likelihood classifier is used. The method also has the ability of lossy data compression since the original data can be reconstructed using the fitted curves. In addition, the proposed algorithm has the possibility to be applied to all pixels of image individually, independently and simultaneously, unlike methods like principal component analysis which need to know all data points to compute the transformation matrix before transforming data points to new feature space.