Recently, the low-rank and sparse decomposition model (LSDM) has been used for anomaly detection in hyperspectral imagery. The traditional LSDM assumes that the sparse component where anomalies and noise reside can be modeled by a single distribution which often potentially confuses weak anomalies and noise. Actually, a single distribution cannot accurately describe different noise characteristics. In this article, a combination of a mixture noise model with low-rank background may more accurately characterize complex distribution. A modified LSDM, by modeling the sparse component as a mixture of Gaussian (MoG), is employed for hyperspectral anomaly detection. In the proposed framework, the variational Bayes (VB) algorithm is applied to infer a posterior MoG model. Once the noise model is determined, anomalies can be easily separated from the noise components. Furthermore, a simple but effective detector based on the Manhattan distance is incorporated for anomaly detection under complex distribution. The experimental results demonstrate that the proposed algorithm outperforms the classic Reed–Xiaoli (RX), and the state-of-the-art detectors, such as robust principal component analysis (RPCA) with RX.

中文翻译：

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用于高光谱异常检测的低秩稀疏分解与高斯混合

最近，低秩稀疏分解模型（LSDM）已被用于高光谱图像中的异常检测。传统的 LSDM 假设异常和噪声所在的稀疏分量可以通过单个分布建模，这通常可能会混淆弱异常和噪声。实际上，单一分布无法准确描述不同的噪声特性。在本文中，混合噪声模型与低秩背景的组合可以更准确地表征复杂分布。通过将稀疏分量建模为高斯 (MoG) 的混合，使用修改后的 LSDM 进行高光谱异常检测。在所提出的框架中，应用变分贝叶斯 (VB) 算法来推断后验 MoG 模型。一旦确定了噪声模型，异常可以很容易地从噪声成分中分离出来。此外，一个简单但有效的基于曼哈顿距离的检测器被结合用于复杂分布下的异常检测。实验结果表明，所提出的算法优于经典的 Reed-Xiaoli (RX) 和最先进的检测器，例如带有 RX 的稳健主成分分析 (RPCA)。