A Geometric Algebra-Based Model for Enhanced Hyperspectral Anomaly Detection

Hyperspectral anomaly detection (HAD) is of great significance in remote sensing by identifying spectrally distinct pixels as anomalies without prior information, while the majority of pixels with similar spectral characteristics are classified as background. While existing approaches combine the strengths of deep learning (DL) in feature extraction and background suppression with the effectiveness of low-rank representation (LRR) in background modeling, they fail to fully exploit rich spatial information and long-range spectral dependencies due to the limitations of conventional convolutional operations. To address this issue, we propose a geometric algebra (GA)-based deep neural network for HAD, named GA-HAD. The network constructs an encoder-decoder architecture using GA convolutional layers to extract spectral-spatial features, capturing multidimensional spatial information while preserving the intricate spectral characteristics of hyperspectral images (HSIs). A specialized reconstruction error is designed to train the GA feature extraction network with high efficiency and accuracy. The encoder features are integrated with the LRR algorithm and a Gaussian mixture model (GMM)-based dictionary to improve background modeling and robustness. Finally, the detection maps output by the low-rank detection module are refined through an edge-preserving filter to produce the final detection result. Extensive experiments on four datasets demonstrate the superiority of our proposed GA-HAD framework in overall detection effect compared to thirteen representative baselines, implying our potential application in the field of HAD.