Robust Tensor Completion via Gradient Tensor Nuclear ℓ 1 - ℓ 2 Norm for Traffic Data Recovery

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. ExistingRobust 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. To address these limitations, we introduce the gradient tensor nuclear$\ell _{1}$-$\ell _{2}$norm via a non-convex tensor rank surrogate and an advanced feature fusion strategy, and integrate it into the RTC framework to propose theRobust Tensor Completion via Gradient Tensor Nuclear$\ell _{1}$-$\ell _{2}$Norm(RTC-GTNLN) model. The proposed model not only fully exploits both global low-rankness and local consistency without a 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. The code is available athttps://github.com/HaoShu2000/RTC-GTNLN