Spectral-Spatial Extraction through Layered Tensor Decomposition for Hyperspectral Anomaly Detection
Quan Yu, Yu-Hong Dai, Minru Bai
TL;DR
This work addresses hyperspectral anomaly detection by integrating spectral and spatial cues within a unified layered tensor decomposition (LTD) framework. Spectral anomalies are extracted with non-negative matrix factorization, while spatial anomalies are captured via low rank tensor representation using a tensor-tubal-rank equivalence to tensor group sparsity regularization. The approach introduces a rank-reduction strategy with validation and a proximal alternating minimization solver with convergence guarantees, achieving strong HAD performance on ABU and MVTec datasets with improved efficiency. The combination of spectral-spatial fusion, a guided image filter for clean detections, and rigorous theory on TGSR equivalence and KL-based convergence underscores the method’s practical impact for robust, scalable HAD in real-world scenarios.
Abstract
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.