# Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recovery

arXiv: https://arxiv.org/abs/2506.22732 · HTML: https://mlsanity.com/paper/2506.22732/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 70 references that are in the map.
- First posted on arXiv 28 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2003.10271/) (2020)
- [Low-Rank Hankel Tensor Completion for Traffic Speed Estimation](https://mlsanity.com/paper/2105.11335/) (2021)
- [Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices](https://mlsanity.com/paper/2201.12592/) (2022)
- [Laplacian Convolutional Representation for Traffic Time Series Imputation](https://mlsanity.com/paper/2212.01529/) (2022)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2008.03194/) (2020)
- [Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns](https://mlsanity.com/paper/2205.09390/) (2022)
- [Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation](https://mlsanity.com/paper/2103.08323/) (2021)
- [Traffic State Estimation from Vehicle Trajectories with Anisotropic Gaussian Processes](https://mlsanity.com/paper/2303.02311/) (2023)
- [An Inexact Accelerated Stochastic ADMM for Separable Convex Optimization](https://mlsanity.com/paper/2010.12765/) (2020)
- [Generalized Symmetric ADMM for Separable Convex Optimization](https://mlsanity.com/paper/1812.03769/) (2018)
- [Generalized Least Squares Kernelized Tensor Factorization](https://mlsanity.com/paper/2412.07041/) (2024)

## Abstract (arXiv)

In real-world scenarios, spatiotemporal traffic data frequently experiences dual degradation from missing values and noise caused by sensor malfunctions and communication failures. Therefore, effective data recovery methods are essential to ensure the reliability of downstream data-driven applications. while classical tensor completion methods have been widely adopted, they are incapable of modeling noise, making them unsuitable for complex scenarios involving simultaneous data missingness and noise interference. Existing Robust Tensor Completion (RTC) approaches offer potential solutions by separately modeling the actual tensor data and noise. However, their effectiveness is often constrained by the over-relaxation of convex rank surrogates and the suboptimal utilization of local consistency, leading to inadequate model accuracy. To address these limitations, we first introduce the tensor L1-L2 norm, a novel non-convex tensor rank surrogate that functions as an effective low-rank representation tool. Leveraging an advanced feature fusion strategy, we further develop the gradient tensor L1-L2 norm by incorporating the tensor L1-L2 norm in the gradient domain. By integrating the gradient tensor nuclear L1-L2 norm into the RTC framework, we propose the Robust Tensor Completion via Gradient Tensor Nuclear L1-L2 Norm (RTC-GTNLN) model, which not only fully exploits both global low-rankness and local consistency without trade-off parameter, but also effectively handles the dual degradation challenges of missing data and noise in traffic data. Extensive experiments conducted on multiple real-world traffic datasets demonstrate that the RTC-GTNLN model consistently outperforms existing state-of-the-art methods in complex recovery scenarios involving simultaneous missing values and noise.