Hyperspectral image anomaly detection faces the challenge of difficulty in annotating anomalous targets. Autoencoder(AE)-based methods are widely used due to their excellent image reconstruction capability. However, traditional grid-based image representation methods struggle to capture long-range dependencies and model non-Euclidean structures. To address these issues, this paper proposes a self-supervised Masked Graph AutoEncoder (MGAE) for hyperspectral anomaly detection. MGAE utilizes a Graph Attention Network (GAT) autoencoder to reconstruct the background of hyperspectral images and identifies anomalies by comparing the reconstructed features with the original features. Specifically, we constructs a topological graph structure of the hyperspectral image, which is then input into the GAT autoencoder for reconstruction, leveraging the multi-head attention mechanism to learn spatial and spectral features. To prevent the decoder from learning trivial solutions, we introduce a re-masking strategy that randomly masks both the input features and hidden representations during training, forcing the model to learn and reconstruct features under limited information, thereby improving detection performance. Additionally, the proposed loss function with graph Laplacian regularization (Twice Loss) minimizes variations in feature representations, leading to more consistent background reconstruction. Experimental results on several real-world hyperspectral datasets demonstrate that MGAE outperforms existing methods.

Graph theory-based techniques have recently been adopted for anomaly detection in hyperspectral images (HSIs). However, these methods rely excessively on the relational structure within the constructed graphs and tend to downplay the importance of spectral features in the original HSI. To address this issue, we introduce graph frequency analysis to hyperspectral anomaly detection (HAD), which can serve as a natural tool for integrating graph structure and spectral features. We treat anomaly detection as a problem of graph frequency location, achieved by constructing a beta distribution-based graph wavelet space, where the optimal wavelet can be identified adaptively for anomaly detection. Initially, a high-dimensional, undirected, unweighted graph is built using the pixels in the HSI as vertices. By leveraging the observation of energy shifting to higher frequencies caused by anomalies, we can dynamically pinpoint the specific Beta wavelet associated with the anomalies' high-frequency content to accurately extract anomalies in the context of HSIs. Furthermore, we introduce a novel entropy definition to address the frequency location problem in an adaptive manner. Experimental results from seven real HSIs validate the remarkable detection performance of our newly proposed approach when compared to various state-of-the-art anomaly detection methods.