Learning Nonconvex Tensor Representation With Generalized Reweighted Sparse Regularization for Hyperspectral Anomaly Detection

Jing Yang, Jianbin Zhao, Lu Chen, Haijun Geng, Pei Zhang

Abstract: Tensor representation (TR) can sensitively perceive the inherent prior structure of hyperspectral images, showing broad prospects in hyperspectral anomaly detection (HAD). However, current models are still limited in effectively representing background and anomaly components therein. First, the depiction of background priors relies on multiple separate regularizers with lenient convex surrogate measures, leading to suboptimal background representation. Second, treating all entries in anomaly component equally diminishes the ability to identify anomaly targets. To address these challenges, we propose a novel TR model termed as NTCTV-GRS, which is characterized by two innovative regularizers. Particularly, for background component, a nonconvex tensor correlated total variation regularizer is developed. It effectively integrates low-rankness and smoothness priors of the background in one unified regularizer. More importantly, it fully considers the physical difference of singular values through a rigorous nonconvex surrogate, ensuring robust background representation. For anomaly component, a generalized reweighted sparse regularizer is formulated by assigning the optimal weight distribution for all entries, which more effectively detects and pinpoints anomaly targets. Comparative experiments on five public datasets are extensively conducted and verify the superiority of the proposed method over existing methods in terms of diverse evaluation metrics.