Low-Rank Spectral–Spatial Super-Resolution of Hyperspectral Images Using KAN-Based GAN

Hyperspectral image (HSI) super-resolution (SR) must enhance spatial detail while preserving per-pixel spectral signatures. Convolutional and adversarial models often favour perceptual sharpness at the cost of spectral fidelity, whereas purely subspace methods underfit nonlinear inter-band relations. We present FBD-KAN, a Factorized Basis Decomposition framework trained adversarially, which couples (i) a low-rank spectral projection/reconstruction path with (ii) Kolmogorov–Arnold Network (KAN) layers specialised for smooth yet nonlinear spectral mappings and (iii) lightweight spatial refinements. The generator employs FastKAN-1D layers to project spectra into a compact latent subspace, a residual spectral block to stabilise and enhance inter-band consistency, and FastKAN-2D with pixel shuffle for spatial upsampling; a bilinear skip stabilises high-frequency content. Training uses a PatchGAN discriminator and a compound objective (L1, adversarial, and Spectral Angle Mapper) to jointly optimise spatial fidelity and spectral accuracy. Across five benchmarks (Salinas, Pavia University, Pavia Centre, Cuprite, CAVE), FBD-KAN attains up to 40.52 dB PSNR with SSIM greater than 0.98 and low SAM, while maintaining competitive parameter efficiency. Qualitative spectra further confirm faithful signature reconstruction. Extensive ablation experiments confirm the necessity of each module in the proposed model. Stress testing under Poisson-Gaussian noise shows stable spatial reconstruction but expected spectral sensitivity under photon-limited conditions. Additional interpretability analysis demonstrated that the model learns physically meaningful subspaces and exposes predictable failure modes. Overall, FBD–KAN provides an accurate, interpretable, and computationally lightweight solution for HSI super-resolution, offering strong potential for real-time and onboard remote-sensing deployment.