Spectral-Spatial Extraction through Layered Tensor Decomposition for Hyperspectral Anomaly Detection

Low rank tensor representation (LRTR) methods are very useful for hyperspectral anomaly detection (HAD). To overcome the limitations that they often overlook spectral anomaly and rely on large-scale matrix singular value decomposition, we first apply non-negative matrix factorization (NMF) to alleviate spectral dimensionality redundancy and extract spectral anomaly and then employ LRTR to extract spatial anomaly while mitigating spatial redundancy, yielding a highly efffcient layered tensor decomposition (LTD) framework for HAD. An iterative algorithm based on proximal alternating minimization is developed to solve the proposed LTD model, with convergence guarantees provided. Moreover, we introduce a rank reduction strategy with validation mechanism that adaptively reduces data size while preventing excessive reduction. Theoretically, we rigorously establish the equivalence between the tensor tubal rank and tensor group sparsity regularization (TGSR) and, under mild conditions, demonstrate that the relaxed formulation of TGSR shares the same global minimizers and optimal values as its original counterpart. Experimental results on the Airport-Beach-Urban and MVTec datasets demonstrate that our approach outperforms state-of-the-art methods in the HAD task.