Hyperspectral anomaly detection is a vital aspect of remote sensing as it focuses on identifying pixels with distinct spectral–spatial properties in comparison to their background representations. However, existing methods for anomaly detection in HSIs often overlook the spatial correlation between pixels by converting the three-dimensional tensor data into its folded form of independent signatures, which may lead to insufficient detection performance. To address this limitation, we develop an anomaly detection algorithm from a tensor representation perspective, which begins by separating the observed hyperspectral image into background and anomaly cubes. We leverage the tensor nuclear norm (TNN) to capture the inherent low-rank structure of background cube globally. This allows us to effectively model and represent the background information. To further improve the detection performance, we introduce spatial–spectral total variation (SSTV) for effectively promoting piecewise smoothness of the background tensor, aiding in the identification of anomalies. Additionally, we incorporate RX-derived attention weights-guided ${\ell }_{2,1}$ norm. This encourages group sparsity of anomalous pixels, improving the precision of anomaly detection. To solve our proposed method, we employ the alternating direction method of multipliers (ADMM), ensuring guaranteed convergence and efficient computation. Through experiments on different kinds of hyperspectral real datasets, we have demonstrated that our method surpasses several state-of-the-art detectors.

高光谱异常检测是遥感的一个重要方面，因为它专注于识别与其背景表示相比具有不同光谱空间特性的像素。然而，现有的 HSI 异常检测方法往往通过将三维张量数据转换为其独立签名的折叠形式而忽略像素之间的空间相关性，这可能导致检测性能不足。为了解决这个限制，我们从张量表示的角度开发了一种异常检测算法，该算法首先将观察到的高光谱图像分离为背景和异常立方体。我们利用张量核范数（TNN）来捕获全局背景立方体固有的低阶结构。这使我们能够有效地建模和表示背景信息。为了进一步提高检测性能，我们引入了空间光谱全变分（SSTV），以有效提高背景张量的分段平滑度，有助于识别异常。此外，我们还结合了 RX 衍生的注意力权重引导${\ell }_{2,1}$规范。这促进了异常像素的群体稀疏性，提高了异常检测的精度。为了解决我们提出的方法，我们采用乘法器交替方向法（ADMM），确保保证收敛和高效计算。通过对不同类型的高光谱真实数据集的实验，我们证明了我们的方法超越了几种最先进的探测器。