Hyperspectral Anomaly Detection Fused Unified Nonconvex Tensor Ring Factors Regularization

In recent years, tensor decomposition-based approaches for hyperspectral anomaly detection (HAD) have gained significant attention in the field of remote sensing. However, existing methods often fail to flexibly and effectively extract both the global correlations and local smoothness of the background components in hyperspectral images (HSIs). To mitigate this critical issue, we put forward a novel HAD method named HAD-EUNTRFR, which incorporates an enhanced unified nonconvex tensor ring (TR) factor regularization. In the HAD-EUNTRFR framework, the raw HSIs are first decomposed into background and anomaly components using the idea of tensor robust principal component analysis. The TR decomposition is then employed to capture the spatial-spectral correlations within the background component. In addition, we introduce a unified and efficient nonconvex regularizer, induced by tensor singular value decomposition (T-SVD), to simultaneously encode the low-rankness and sparsity of the 3-D gradient TR factors into a unique concise form. The above characterization scheme enables the interpretable gradient TR factors to inherit the low-rankness and smoothness of the original background. To further enhance anomaly detection, we design a generalized nonconvex regularization term to exploit the group sparsity of the anomaly component. Based upon the above, we ultimately propose a scalable and reliable nonconvex HAD model. To solve the resulting doubly nonconvex model, we develop a highly efficient optimization algorithm based on the alternating direction method of multipliers (ADMM) framework. Theoretical results on convergence analysis for the proposed algorithm are derived. Experimental results on several benchmark datasets demonstrate that our proposed method outperforms existing state-of-the-art (SOTA) approaches in terms of detection accuracy.