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

This paper presents a novel kernel-based decomposition model with total variation and sparsity regularizations via union dictionary for nonlinear hyperspectral anomaly detection. It decomposes a hyperspectral imagery into three components: background, anomaly, and noise. By using a union dictionary consisting of background and potential anomalous pixels, each test pixel can be well represented. Further, by utilizing endmember-kernel theory to handle nonlinear interactions between atoms in the dictionary, the complex light scattering effects can be effectively characterized. Besides, to separate these components effectively, the total variation and sparsity regularizations are incorporated into the decomposition model to represent the spatial properties of the background and the anomaly, respectively. The experimental results on simulated and real hyperspectral data sets demonstrated the effectiveness of our proposed method compared to several conventional and state-of-the-art anomaly detection methods.