Low-Rank and Sparse Decomposition with Mixture of Gaussian for Hyperspectral Anomaly Detection

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.