A novel approach to hyperspectral data feature extraction using rational function curve fitting

Regarding to large volumes of hyperspectral data that contain hundreds of spectral bands and due to their very high between-band correlation, feature reduction (either feature selection or extraction) is an essential part of classification process for this data type. Many feature reduction techniques have been developed by considering different specifications of hyperspectral data in spectral and spatial domains. In this paper, a feature reduction technique based on extracting new features is proposed. For each pixel of a hyperspectral image, a specific rational function approximation is developed to fit the spectral response curve of that pixel. Coefficients of the numerator and denominator of the rational function are considered as new extracted features. This new method relies on the fact that the sequence discipline - ordinance of reflectance coefficients in spectral response curve - contains some information which has not been addressed by other competing methods that are based on statistical analysis of data, such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) and their nonlinear versions. In addition, we show that naturally different curves can be approximated by rational functions with equal form, but different amounts of coefficients. Maximum likelihood classification results demonstrate that the Rational Function Curve Fitting Feature Extraction (RFCF-FE) method provides better classification accuracies compared to competing feature extraction algorithms. In addition, the proposed algorithm has the possibility to be applied to all pixels of image individually and simultaneously, unlike to PCA and other methods which need to transform whole data to new feature space.