Kernel-Based Nonlinear Anomaly Detection via Union Dictionary for Hyperspectral Images

Anomaly detection has been known to be an important issue in hyperspectral remote sensing applications. It aims to detect anomalous targets whose spectral signatures are very different from the background pixels. Although many linear detectors have obtained acceptable detection results, the linear model might not be able to describe complex hyperspectral data and could be replaced by nonlinear models. In this article, we investigate the intrinsic nonlinear characteristics of hyperspectral images (HSIs) on basis of the nonlinear mixing models and propose a novel nonlinear hyperspectral anomaly detection method based on kernel theory and union dictionary. First, the global strong anomalies in the scene and the local background pixels are utilized to construct a union dictionary. Then, a nonlinear representation-based anomaly detection model with the constructed union dictionary is designed, in which the nonlinear mixing effect of HSIs is considered. Meanwhile, the kernel theory is exploited to deal with the nonlinear interactions among the atoms in the dictionary. Finally, the anomalous level of a test pixel is determined by the representation coefficients associated with the anomaly dictionary. The proposed method is evaluated on both synthetic and real hyperspectral datasets. Experimental results demonstrate its excellent performance in comparison with linear and nonlinear state-of-the-art anomaly detectors.