Graph and Total Variation Regularized Low-Rank Representation for Hyperspectral Anomaly Detection

Anomaly detection is of great importance among hyperspectral applications, which aims at locating targets that are spectrally different from their surrounding background. A variety of anomaly detection methods have been proposed in the past. However, most of them fail to take the high spectral correlations of all the pixels into consideration. Low-rank representation (LRR) has drawn a great deal of interest in recent years, as a promising model to exploit the intrinsic low-rank property of hyperspectral images. Nevertheless, the original LRR model only analyzes the spectral signatures without taking advantage of the valuable spatial information in hyperspectral images. Furthermore, it has been shown that the local geometrical information of the hyperspectral data is also important for discrimination between the anomalies and background pixels. In this article, we incorporate the graph regularization and total variation (TV) regularization into the LRR formulation and propose a novel anomaly detection method based on graph and TV regularized LRR (GTVLRR) model, to preserve the local geometrical structure and spatial relationships in hyperspectral images. Extensive experiments have been conducted on both simulated and real hyperspectral data sets. The experimental results demonstrate the superiority of the proposed method over conventional and state-of-the-art anomaly detection methods.