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

Abstract

Low rank tensor representation (LRTR) methods are very useful for hyperspectral anomaly detection (HAD). However, existing LRTR methods often overlook spectral anomaly and rely on computationally expensive large-scale matrix singular value decomposition. To overcome these limitations, we propose a highly efficient layered tensor decomposition (LTD) framework that simultaneously optimizes two key components within a unified model:Layer 1, which reduces spectral redundancy and extracts spectral anomaly, and Layer 2, which captures spatial low rank features and extracts spatial anomaly. The resulting spectral and spatial anomaly maps are then integrated to achieve a robust final detection result. 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.

Quan Yu

PhD student

My research interests include low rank tensor optimization, image processing and machine learning.