Orthogonal polynomial function fitting for hyperspectral data representation and discrimination

In this paper, we propose an efficient method based on orthogonal polynomial function (OPF) fitting for hyperspectral remote sensing data representation and discrimination. Given a spectral signature, it is first divided into spectral segments by a splitting strategy. Then, the extracted segments are fitted via OPF fitting. The fitting coefficients of the input spectrum are selected for data representation and discrimination. To validate the usefulness of the proposed method, laboratory spectra and real hyperspectral data were selected for experimental analysis. The results showed that our method can efficiently mine geometric structural information of spectral signatures and compress them into a few fitting parameters. These parameters can be used to sparsely represent the input spectra and effectively distinguish different spectral signatures. In terms of representation, the proposed method is superior to the traditional inverse Gaussian function (IGF) model. Moreover, the OPF sparse feature exhibits better performance than the typical wavelet-based method in terms of achieving a trade-off between feature length and reconstruction error. Furthermore, the use of an optimized nonlinear SVM classifier shows that the discriminative ability for OPF normal features generally improves as the feature length increases and become relatively stable after the length reaches 30. Also the OPF features with the length of 30 can achieve comparable overall accuracies for the original bands and the typical wavelet-based features. As our method is data dependent, the optimal parameter value may vary for different data. In addition, the proposed feature extraction method is very fast and improves the computational efficiency significantly. Overall, the proposed method has considerable potential from the perspective of hyperspectral data analysis.