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

arXiv: https://arxiv.org/abs/2503.05183 · HTML: https://mlsanity.com/paper/2503.05183/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 63 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 8 of 8)

- [More Diverse Means Better: Multimodal Deep Learning Meets Remote Sensing Imagery Classification](https://mlsanity.com/paper/2008.05457/) (2020)
- [Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery](https://mlsanity.com/paper/1911.05774/) (2019)
- [Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion](https://mlsanity.com/paper/2110.08774/) (2021)
- [Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation](https://mlsanity.com/paper/1710.05705/) (2017)
- [Hyperspectral Image Denoising and Anomaly Detection Based on Low-rank and Sparse Representations](https://mlsanity.com/paper/2103.07437/) (2021)
- [Euclidean-Norm-Induced Schatten-p Quasi-Norm Regularization for Low-Rank Tensor Completion and Tensor Robust Principal Component Analysis](https://mlsanity.com/paper/2012.03436/) (2020)
- [Multi-Tubal Rank of Third Order Tensor and Related Low Rank Tensor Completion Problem](https://mlsanity.com/paper/2012.05065/) (2020)
- [Tensor factorization based method for low rank matrix completion and its application on tensor completion](https://mlsanity.com/paper/2201.09197/) (2022)

## Built on by (most cited first, 2 of 2)

- [A Multi-View Coupled Tensor Decomposition for Lightweight Online Adaptive Traffic Prediction](https://mlsanity.com/paper/2608.25498/) (2026)
- [Hyperspectral Anomaly Detection via Group Sparse Low-Rank Tensor Factorization With Automatic Anomaly Grouping](https://mlsanity.com/paper/2609.08121/) (2026)

## Abstract (arXiv)

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.