Wavelet-based diffusion with spatial-frequency attention for hyperspectral anomaly detection

Frequency decomposition offers a promising approach for hyperspectral anomaly detection (HAD) by separating anomalies from redundant backgrounds. However, an improper decomposition strategy may cause domain shifts in the low-frequency component (LFC) and excessive suppression of the high-frequency component (HFC), ultimately affecting detection performance. To address those challenges, we propose a novel frequency decomposition framework wavelet-enhanced diffusion framework for HAD, termed as WDHAD. Following a 2D discrete wavelet transformation, the LFC and HFC are processed in parallel: 1) The LFC is handled via a Low-Frequency Diffusion Model (LFDM), which employs a Low-Frequency Denoising Autoencoder (LFDAE) with spatial-frequency attention to recover key features and remove background noise. 2) The HFC is processed through a High-Frequency Enhancement Module (HFEM) that preserves edges and textures to improve anomaly detection. Both components are then fused and passed through a 2D inverse wavelet transformation, with the detection map obtained by a Reed-Xiaoli detector. In addition, a negative log-likelihood noise loss is introduced to model uncertainty. Extensive experiments on six public and two real-world UAV datasets demonstrate that WDHAD achieves robust generalization and cross-domain adaptability. The code will be publicly available at https://github.com/CZhu0066/WDHAD . • This work proposes a wavelet-based diffusion model for hyperspectral anomaly detection. • This work combines the spatial and frequency dual-domain features. • This work introduces the negative log-likelihood noise loss function. • Extensive experiments validate robustness and cross-domain adaptability.