HAD-MSF: Multi-domain neural fusion with state-space and graph modeling for hyperspectral anomaly detection

Hyperspectral anomaly detection (HAD) remains challenging because spatial, spectral, and frequency dependencies coexist and exhibit heterogeneous characteristics. Existing CNN-, Transformer-, and GCN-based approaches often rely on a single modeling paradigm, which may limit their ability to fully exploit these complementary structures. In this work, we propose HAD-MSF, a neural reconstruction framework that integrates multiple domain-specific representations within a unified architecture. An Adaptive Wavelet Approximation Transform (AdaWAT) separates hyperspectral cubes into low- and high-frequency components, which are processed by a state-space-driven Spatial-Frequency Mamba module to capture long-range dependencies with linear complexity. In parallel, a Spatial-Spectral Graph Convolution branch models pixel topology together with inter-band correlations, enhancing spectral discrimination. A lightweight gating mechanism adaptively fuses the two representations into a compact reconstruction network, where anomalies are identified from residuals. Experiments on three remote sensing and two medical hyperspectral datasets show that HAD-MSF achieves consistently competitive detection performance with relatively low arithmetic complexity. Additional analyses on component design, threshold selection, robustness, cross-scene transfer, and full-band settings further characterize the effectiveness and practical properties of the proposed framework. These results demonstrate the effectiveness of integrating wavelet, state-space, and graph modeling for hyperspectral anomaly detection.