Conventional deep networks for hyperspectral image (HSI) classification often rely on large labeled datasets and computationally intensive optimization procedures. In this talk, we introduce an analytic deep framework for HSI feature extraction based on stochastic adaptive Fourier decomposition (SAFD) and partial differential equation (PDE)-driven feature propagation. Specifically, convolutional kernels are constructed analytically using SAFD, a greedy Hardy-space decomposition method that captures intrinsic oscillatory structures from downsampled inputs at each layer. To recover spatial resolution and enhance structural consistency, a PDE-based upsampling operator derived from Perona–Malik anisotropic diffusion is introduced to reconstruct feature maps progressively across scales. By stacking multiple such layers, the proposed framework forms a hierarchical multi-scale representation for hyperspectral data analysis. Extensive experiments on three benchmark HSI datasets under a five-shot-per-class protocol demonstrate that the proposed method consistently achieves superior classification performance with significantly reduced computational cost. Compared with state-of-the-art few-shot learning approaches, the proposed framework delivers improved accuracy while maintaining high efficiency and robustness.

Liming Zhang received the B.S. degree in Computer Software at Nankai University, China and M.S. degree in Signal Processing at Nanjing University of Science and Technology, China. She received her PhD degree in image processing at University of New England, Australia. She is currently an assistant professor in Faculty of Science and Technology, University of Macau. Her research interests include Computer vision, Image processing, Artificial intelligence, Machine learning, and Deep learning. She has published over 100 papers, including IEEE Transactions on Image Processing, IEEE Transactions on Signal Processing, CVPR, ect. The main contribution lies on new image and signal processing methodology – adaptive Fourier decomposition (AFD)based image processing methods and new deep network development. The image and video compression results based on stochastic AFD (SAFD) exceed the current international image and video compression standards JPEG, JPEG2000, MPEG, and also exceed the compression results of the popular deep networks. SAFD-based deep networks also perform well in alleviating the scarcity of training data.