Kernel-Based Decomposition Model With Total Variation and Sparsity Regularizations via Union Dictionary for Nonlinear Hyperspectral Anomaly Detection

Many linear approaches have been extensively proposed for the anomaly detection problem in hyperspectral images (HSIs), while nonlinear approaches have been rarely studied although most practical cases are nonlinear. Moreover, these existing nonlinear methods simply nonlinearly map each pixel into a high-dimensional space, which does not describe complex light scattering effects between endmembers. To address the above issues, this article proposes an endmember-kernel-based decomposition model with total variation (TV) and sparsity regularizations via a union dictionary for the nonlinear anomaly detection in HSIs. The proposed decomposition model utilizes endmember-kernel theory to handle nonlinear interactions between atoms in the dictionary, allowing for the effective characterization of complex light scattering effects. By using this endmember-kernel-based decomposition model, hyperspectral imagery can be decomposed into three components: anomaly, background, and noise. To separate these components effectively, the TV and sparsity regularizations are incorporated into the decomposition model to characterize the spatial properties of the background and the anomaly, respectively. Besides, we present a novel construction framework of union dictionary that combines superpixel segmentation and clustering methods sequentially to achieve more accurate dictionary representation capabilities. Finally, the anomalous level of a tested pixel is calculated by the abundances associated with the anomaly dictionary. The experimental results on both synthetic and real hyperspectral datasets demonstrate that the proposed method outperforms several linear and nonlinear state-of-the-art anomaly detectors.