Spatial–Spectral Total Variation-Regularized Low-Rank Tensor Representation for Hyperspectral Anomaly Detection

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.