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.

中文翻译：

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基于改进的低秩稀疏表示和联合高斯混合分布的高光谱图像异常检测

基于低秩稀疏表示（LRASR）的高光谱图像异常检测中使用的背景字典包含目标信息和背景信息，这将导致低检测精度。针对这一问题，本文提出了一种基于低秩稀疏表示和联合高斯混合分布（MOG-LRASR）的改进高光谱异常检测算法。在传统的低秩和稀疏分解模型中将稀疏分量建模为高斯（MOG）分布的混合，可以获得更纯的低秩背景分量。然后使用低秩背景分量作为字典学习的输入得到待检测的稀疏矩阵。由于异常部分的分布通常是稀疏而复杂的，本文中使用曼哈顿距离来评估异常像素。使用Wilcoxon秩和检验，实验结果表明本文提出的算法得分最高，证明MOG-LRASR比其他算法具有更高的检测稳定性。此外，它在实验表明的其他数据集上也取得了更好的检测结果。