Hyperspectral Anomaly Detection Based on Adaptive Low-Rank Transformed Tensor

Hyperspectral anomaly detection, which is aimed at distinguishing anomaly pixels from the surroundings in spatial features and spectral characteristics, has attracted considerable attention due to its various applications. In this article, we propose a novel hyperspectral anomaly detection algorithm based on adaptive low-rank transform, in which the input hyperspectral image (HSI) is divided into a background tensor, an anomaly tensor, and a noise tensor. To take full advantage of the spatial&#x2013;spectral information, the background tensor is represented as the product of a transformed tensor and a low-rank matrix. The low-rank constraint is imposed on frontal slices of the transformed tensor to depict the spatial&#x2013;spectral correlation of the HSI background. Besides, we initialize a matrix with predefined size and then minimize its <inline-formula> <tex-math notation="LaTeX">$l_{2.1}$</tex-math> </inline-formula>-norm to adaptively derive an appropriate low-rank matrix. The anomaly tensor is constrained with the <inline-formula> <tex-math notation="LaTeX">$l_{2.1.1}$</tex-math> </inline-formula>-norm to depict the group sparsity of anomalous pixels. We integrate all regularization terms and a fidelity term into a non-convex problem and develop a proximal alternating minimization (PAM) algorithm to solve it. Interestingly, the sequence generated by the PAM algorithm is proven to converge to a critical point. Experimental results conducted on four widely used datasets demonstrate the superiority of the proposed anomaly detector over several state-of-the-art methods.