DF\(^2\)Net: deformable fourier filter network for hyperspectral image classification

MLP-like architectures in hyperspectral image (HSI) classification flourish recently. However, these methods face challenges such as insufficient spectral-spatial feature extraction capability and excessive consumption of network computing resources. To address these problems, a deformable Fourier filter network (DF\(^{\varvec{2}}\)Net) is proposed as an innovative lightweight MLP framework for HSI classification. DF\(^{\varvec{2}}\)Net employs Fourier transform filters and spatial deformable operations to efficiently capture spectral-spatial features while maintaining a lightweight design. Specifically, two modules in DF\(^{\varvec{2}}\)Net are developed to extract and facilitate the deep integration of spectral-spatial features, namely the spectral discrete Fourier transform filter (SeDFT) module and the spatial deformable discrete Fourier transform filter (SaD\(^{\varvec{2}}\)FT) module. The SeDFT module employs a one-dimensional discrete Fourier transform filter (1D\(^{\varvec{2}}\)FT) to extract spectral features in the frequency domain, effectively capturing detailed information from the original spectrum. Additionally, the parameter-free design of the SeDFT module streamlines the feature processing pipeline and improves computational efficiency. The SaD\(^{\varvec{2}}\)FT module performs a two-dimensional deformable discrete Fourier transform (2D\(^{\varvec{3}}\)FT) filter, enabling low-parameter feature extraction by transforming spatial features into frequency domain representations. Moreover, the spatial deformable operation enhances the capacity of the network to perceive spatial structural variations by introducing learnable offsets. Experimental results on four public HSI datasets demonstrate that DF\(^{\varvec{2}}\)Net consistently achieves superior performance in lightweight classification. Compared to other state-of-the-art models, DF\(^{\varvec{2}}\)Net significantly reduces both the number of parameters and computational resource requirements while preserving high performance.