A Low-Rank and Sparse Matrix Decomposition-Based Mahalanobis Distance Method for Hyperspectral Anomaly Detection

Anomaly detection is playing an increasingly important role in hyperspectral image (HSI) processing. The traditional anomaly detection methods mainly extract knowledge from the background and use the difference between the anomalies and the background to distinguish them. Anomaly contamination and the inverse covariance matrix problem are the main difficulties with these methods. The low-rank and sparse matrix decomposition (LRaSMD) technique may have the potential to solve the aforementioned hyperspectral anomaly detection problem since it can extract knowledge from both the background and the anomalies. This paper proposes an LRaSMD-based Mahalanobis distance method for hyperspectral anomaly detection (LSMAD). This approach has the following capabilities: 1) takes full advantage of the LRaSMD technique to set the background apart from the anomalies; 2) explores the low-rank prior knowledge of the background to compute the background statistics; and 3) applies the Mahalanobis distance differences to detect the probable anomalies. Extensive experiments were carried out on four HSIs, and it was found that LSMAD shows a better detection performance than the current state-of-the-art hyperspectral anomaly detection methods.