Generalized Nonconvex Low-Rank Tensor Representation for Hyperspectral Anomaly Detection

Low-rank tensor representation (LRTR) methods have attracted great interest for their powerful ability to separate backgrounds and anomalies. However, most of the current LRTR models use the popular and convex surrogate tensor nuclear norm (TNN) to solve optimization problems, which results in a loose approximation and suboptimal solver for the original problem. Besides, most existing methods solve the nonconvex optimization problems case-by-case, consequently losing one unified solver. To solve the above issues, we propose the generalized nonconvex low-rank tensor representation (GNLTR) for hyperspectral anomaly detection (HAD), a unified solver not case-by-case one of existing nonconvex optimization problems. Compared to the TNN, GNLTR contains many popular nonconvex penalty functions as tighter regularizers of the tensor tubal rank to constrain the low rank of the background. Moreover, the $L_{2,1}$ norm has been integrated into the GNLTR model for the sparse anomalies. For the optimization problem, it is handled quickly and efficiently through a well-organized alternating direction method of multipliers (ADMM). The experiments on several real-world hyperspectral datasets demonstrate the superior performance of the GNLTR model in comparison with some state-of-the-art anomaly detection (AD) models.