A Low-Rank and Sparse Matrix Decomposition- Based Dictionary Reconstruction and Anomaly Extraction Framework for Hyperspectral Anomaly Detection

Abstract

As one of the important applications of hyperspectral imagery (HSI) processing, the Mahalanobis distance-based detector in anomaly detection used to extract knowledge from the background and then calculate the Mahalanobis distance to obtain the detection result. Different from the previous work, a novel low-rank and sparse matrix decomposition (LRaSMD)-based dictionary reconstruction and anomaly extraction framework constructs the detector by a comprehensive combination of the low-rank and sparse matrix for hyperspectral anomaly detection. We use the LRaSMD to fully exploit the background and sparse information to construct the detector. For the low-rank part, we use atom usage probability to reconstruct the dictionary for follow-up collaborative representation (CR). For the sparse part, we calculate the Euclidean distance and get the result by using a ratio to add these two parts. The proposed algorithm was tested on three real-world HSI data sets and demonstrated outstanding detection performance when compared with other state-of-the-art detectors.