Low-Rank and Sparse Matrix Decomposition With Orthogonal Subspace Projection-Based Background Suppression for Hyperspectral Anomaly Detection

Although the low-rank and sparse matrix decomposition (LRaSMD)-based anomaly detectors can effectively extract the low-rank structure as the background component and the sparse structure as the anomaly component for anomaly detection (AD) while simultaneously considering the additive noise, the background interferences in the sparse component remain a serious problem that will increase the false alarm rate and influence the detection of real anomalies. To alleviate this issue, a novel LRaSMD with orthogonal subspace projection (OSP)-based background suppression and adaptive weighting for hyperspectral AD is proposed in this letter. Based on the fact that the background interferences in the sparse component are mainly some sparse objects with slight spectral differences from the main background, the OSP is employed to project the sparse component into the background orthogonal subspace that is estimated from the low-rank component to suppress the background interferences and highlight the anomalies. Furthermore, the low-rank component provides an effective estimation of the background statistics, which can be used to adaptively weigh the detection results. Experiments on both synthetic and real hyperspectral data sets demonstrate the effectiveness of the proposed algorithm.