Orthogonal Rational Basis-Function-Based Discriminant Analysis for Hyperspectral Image Classification

This paper presents a nonlinear discriminant analysis (NDA) method based on an orthogonal rational function (ORF) system for the classification of hyperspectral images (HSI). The proposed method, abbreviated ORF-NDA, is formulated from the standpoint of function theory. It can make good use of the spectral curve characteristics of HSIs and establish a methodology more suitable for HSI processing in the function space. This is a new paradigm that is different from mainstream hyperspectral data processing methods. First, a functional data fitting model based on an adaptive ORF system is designed for the reconstruction of the spectral curve for each pixel in HSIs. Second, the stochastic adaptive Fourier decomposition (SAFD) method is used to find the optimal parameters for building the adaptive ORF system. Third, based on the reconstructed spectral curve, an NDA method based on an ORF system is built for feature extraction of HSIs. Finally, a spectral-spatial classification framework is designed for HSIs in scenarios with limited sample sizes. Experimental results on five public HSIs demonstrate that the proposed ORF-NDA method outperforms several state-of-the-art deep learning methods in classification accuracy.