Exploiting Weighted Multidirectional Sparsity for Prior Enhanced Anomaly Detection in Hyperspectral Images

Anomaly detection (AD) is an important topic in remote sensing, aiming to identify unusual or abnormal features within the data. However, most existing low-rank representation methods usually use the nuclear norm for background estimation, and do not consider the different contributions of different singular values. Besides, they overlook the spatial relationships of abnormal regions, particularly failing to fully leverage the 3D structured information of the data. Moreover, noise in practical scenarios can disrupt the low-rank structure of the background, making it challenging to separate anomaly from the background and ultimately reducing detection accuracy. To address these challenges, this paper proposes a weighted multidirectional sparsity regularized low-rank tensor representation method (WMS-LRTR) for AD. WMS-LRTR uses the weighted tensor nuclear norm for background estimation to characterize the low-rank property of the background. Considering the correlation between abnormal pixels across different dimensions, the proposed method introduces a novel weighted multidirectional sparsity (WMS) by unfolding anomaly into multimodal to better exploit the sparsity of the anomaly. In order to improve the robustness of AD, we further embed a user-friendly plug-and-play (PnP) denoising prior to optimize the background modeling under low-rank structure and facilitate the separation of sparse anomalous regions. Furthermore, an effective iterative algorithm using alternate direction method of multipliers (ADMM) is introduced, whose subproblems can be solved quickly by fast solvers or have closed-form solutions. Numerical experiments on various datasets show that WMS-LRTR outperforms state-of-the-art AD methods, demonstrating its better detection ability.