Hyperspectral Image Classification Based on Fractional Fourier Transform

To effectively utilize the rich spectral information of hyperspectral remote sensing images (HRSIs), the fractional Fourier transform (FRFT) feature of HRSIs is proposed to reflect the time-domain and frequency-domain characteristics of a spectral pixel simultaneously, and an FRFT order selection criterion is also proposed based on maximizing separability. Firstly, FRFT is applied to the spectral pixels, and the amplitude spectrum is taken as the FRFT feature of HRSIs. The FRFT feature is mixed with the pixel spectral to form the presented spectral and fractional Fourier transform mixed feature (SF2MF), which contains time–frequency mixing information and spectral information of pixels. K-nearest neighbor, logistic regression, and random forest classifiers are used to verify the superiority of the proposed feature. A 1-dimensional convolutional neural network (1D-CNN) and a two-branch CNN network (Two-CNNSF2MF-Spa) are designed to extract the depth SF2MF feature and the SF2MF-spatial joint feature, respectively. Moreover, to compensate for the defect that CNN cannot effectively capture the long-range features of spectral pixels, a long short-term memory (LSTM) network is introduced to be combined with CNN to form a two-branch network C-CLSTMSF2MF for extracting deeper and more efficient fusion features. A 3D-CNNSF2MF model is designed, which firstly performs the principal component analysis on the spa-SF2MF cube containing spatial information and then feeds it into the 3-dimensional convolutional neural network 3D-CNNSF2MF to extract the SF2MF-spatial joint feature effectively. The experimental results of three real HRSIs show that the presented mixed feature SF2MF can effectively improve classification accuracy.