# Hyperspectral Anomaly Detection Fused Unified Nonconvex Tensor Ring Factors Regularization

arXiv: https://arxiv.org/abs/2505.17881 · HTML: https://mlsanity.com/paper/2505.17881/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 102 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 14 of 14)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration](https://mlsanity.com/paper/2010.12921/) (2020)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems](https://mlsanity.com/paper/1303.4434/) (2013)
- [Recent Advances and New Guidelines on Hyperspectral and Multispectral Image Fusion](https://mlsanity.com/paper/2008.03426/) (2020)
- [Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices](https://mlsanity.com/paper/2201.12592/) (2022)
- [Hyperspectral Image Classification with Markov Random Fields and a Convolutional Neural Network](https://mlsanity.com/paper/1705.00727/) (2017)
- [Hyperspectral Super-Resolution via Coupled Tensor Ring Factorization](https://mlsanity.com/paper/2001.01547/) (2020)
- [Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation](https://mlsanity.com/paper/2305.11495/) (2023)
- [Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing](https://mlsanity.com/paper/2205.03798/) (2022)
- [Graph Laplacian for Image Anomaly Detection](https://mlsanity.com/paper/1802.09843/) (2018)
- [ERX: A Fast Real-Time Anomaly Detection Algorithm for Hyperspectral Line Scanning](https://mlsanity.com/paper/2408.14947/) (2024)

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

- [Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computation](https://mlsanity.com/paper/2602.12982/) (2026)
- [Hyperspectral Anomaly Detection via Group Sparse Low-Rank Tensor Factorization With Automatic Anomaly Grouping](https://mlsanity.com/paper/2609.08121/) (2026)

## Abstract (arXiv)

In recent years, tensor decomposition-based approaches for hyperspectral anomaly detection (HAD) have gained significant attention in the field of remote sensing. However, existing methods often fail to fully leverage both the global correlations and local smoothness of the background components in hyperspectral images (HSIs), which exist in both the spectral and spatial domains. This limitation results in suboptimal detection performance. To mitigate this critical issue, we put forward a novel HAD method named HAD-EUNTRFR, which incorporates an enhanced unified nonconvex tensor ring (TR) factors regularization. In the HAD-EUNTRFR framework, the raw HSIs are first decomposed into background and anomaly components. The TR decomposition is then employed to capture the spatial-spectral correlations within the background component. Additionally, we introduce a unified and efficient nonconvex regularizer, induced by tensor singular value decomposition (TSVD), to simultaneously encode the low-rankness and sparsity of the 3-D gradient TR factors into a unique concise form. The above characterization scheme enables the interpretable gradient TR factors to inherit the low-rankness and smoothness of the original background. To further enhance anomaly detection, we design a generalized nonconvex regularization term to exploit the group sparsity of the anomaly component. To solve the resulting doubly nonconvex model, we develop a highly efficient optimization algorithm based on the alternating direction method of multipliers (ADMM) framework. Experimental results on several benchmark datasets demonstrate that our proposed method outperforms existing state-of-the-art (SOTA) approaches in terms of detection accuracy.