Tensor Ring Decomposition-Based Generalized and Efficient Nonconvex Approach for Hyperspectral Anomaly Detection

Anomaly detection in hyperspectral images (HSIs) aims to identify sparse, interesting anomalies against the background, which has become a significant topic in remote sensing. Although existing tensor-based methods have achieved commendable performance to some extent, there is still room for further improvement. In combination with three key techniques, i.e., gradient map based modeling, circular tensor ring (TR) unfolding and nonconvex regularization, this paper proposes a novel generalized nonconvex method for hyperspectral anomaly detection (HAD) tasks within the TR framework. For the implementation of our proposed approach, abbreviated as TR-GNHAD, we first develop an effective and reliable HAD model in virtue of two newly unified nonconvex regularizers. The first regularizer is devised under a new prior characterization paradigm, which has a strong ability to encode two insightful prior information underlying the HSI's background simultaneously, i.e., global low-rankness and local smoothness. The other regularizer can well capture the structured sparsity of the abnormal component. Then, we derive an efficient optimization algorithm to solve the proposed model based on the alternating direction method of multipliers (ADMM) framework. Experiments conducted on twelve HSI datasets illustrate that the proposed approach achieves highly competitive performance in both qualitative and quantitative metrics compared with several state-of-the-art HAD methods.