Anomaly Detection in Hyperspectral Images Using Adaptive Graph Frequency Location

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.