Enhanced RX-Based Hyperspectral Anomaly Detection Using Laplacian-Regularized PCA

Hyperspectral anomaly detection application is essential in numerous different remote sensing applications, where the detection of rare and unknown targets in complex scenes is needed. The proposed anomaly detection method in this study is called L-PCAD (Laplacian PCA-based anomaly detection), which plans to combine a Linearized Alternating Direction method (LADM)-based subspace recovery algorithm with a modified RX detector to improve detection accuracy and stability. It starts with an LADM-based approach as a preprocessing stage to get a matrix with rich information relating to anomalies. The resulting low-rank background matrix is subsequently utilized as a guide for the anomaly detection process. In order to enhance the RX detector, the covariance estimation is reformulated using a graph Laplacian constructed from the low-rank background matrix. Instead of directly using the empirical covariance matrix, a normalized Laplacian is computed and subsequently transformed via principal component analysis (PCA) to obtain a stable diagonal representation. This PCA-regularized Laplacian replaces the conventional covariance matrix in the RX formulation while preserving the local spatial structure. The extensive testing of different hyperspectral datasets shows that the proposed approach provides better overall results for detection performance as compared to other hyperspectral anomaly detectors that are the state of the art.