Low-rank and sparse matrix decomposition with background position estimation for hyperspectral anomaly detection

Hyperspectral anomaly detection (AD) has attracted much attention over the last 20 years. It distinguishes pixels with significant spectral differences from the background without any prior knowledge. The low-rank and sparse matrix decomposition (LRaSMD)-based detector has been applied to AD, where the anomaly value is measured by Euclidean distance based on the sparse component. However, the background interference in sparse component seriously increases the false alarm rate and influences the detection of real anomalies. In this paper, a novel AD method based on LRaSMD and background position estimation is proposed, which aims to suppress background interference in the sparse component for a better separation between background and anomalies. Firstly, the original sparse matrix is obtained using the traditional LRaSMD method. Secondly, the abundance maps are constructed by the sequential maximum angel convex cone (SMACC) endmember extraction model. Thirdly, considering that the anomalies occupy only a few pixels with a low probability, the coordinate positions of background pixels are estimated through these abundance maps. Finally, the spectra corresponding to these positions in the original sparse matrix are replaced with zero vectors, and the final anomaly value is calculated based on the improved sparse matrix. The proposed method achieves an outstanding performance by considering both the spectral and spatial characteristics of anomalies. Experimental results on synthetic and real-world hyperspectral datasets demonstrate the superiority of the proposed method compared with several state-of-the-art AD detectors.