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 the following 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.

Publication:

SIAM JOURNAL ON IMAGING SCIENCES

http://dx.doi.org/10.1137/25M1755679

Author:

Yu, Quan

Hunan Univ, Sch Math, Changsha 410082, Peoples R China;

Email address:quanyu@hnu.edu.cn

Bai, Minru (corresponding author)

Hunan Univ, Sch Math, Changsha 410082, Peoples R China

Email address:minru-bai@hnu.edu.cn

Dai, Yu-Hong

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

Email address:dyh@lsec.cc.ac.cn