Application of Curve Fitting in Hyperspectral Data Classification and Compression

Regarding to the high between-band correlation and large volumes of hyperspectral data, feature reduction (either feature selection or extraction) is an important part of classification process for this data type. A variety of feature reduction methods have been developed using spectral and spatial domains. In this paper, a feature extracting technique is proposed based on rational function curve fitting. 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 polynomials of these functions are considered as new extracted features. This new technique is based on the fact that the sequence discipline ordinance of reflectance coefficients in spectral response curve contains some information which has not been considered by other statistical analysis based methods, such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) and their nonlinear versions. Also, 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. The method, also, has the ability of lossy data compression. 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 and simultaneously, unlike to PCA and other methods which need to know whole data for computing the transform matrix.