Anomaly Detection for Hyperspectral Images Based on Improved Low-Rank and Sparse Representation and Joint Gaussian Mixture Distribution

The background dictionary used in the hyperspectral images anomaly detection based on low-rank and sparse representation (LRASR) contains both target information and background information which will result in low detection accuracy. In response to this problem, this article proposes an improved hyperspectral anomaly detection algorithm that is based on low-rank and sparse representation and joint Gaussian mixture distribution (MOG-LRASR). Modeling the sparse components as a mixture of Gaussian (MOG) distribution in the traditional low-rank and sparse decomposition model can get a purer low-rank background component. Then using the low-rank background component as the input of the dictionary learning to get the sparse matrix to be detected. Since the distribution in the anomalous part is usually sparse and complex, Manhattan distance is used to evaluate anomalous pixels in this article. Using Wilcoxon rank-sum test, the experimental results show that the algorithm proposed in this article has the highest score, which proves the MOG-LRASR has higher detection stability than other algorithms. Also, it has achieved better detection results on other data sets indicated by the experiments.