Low-Rank and Deep Plug-and-Play Priors for Missing Traffic Data Imputation

The development of sensor technology has resulted in the accumulation of extensive spatiotemporal traffic information, which holds great potential for predicting traffic patterns and improving traffic management strategies. Nevertheless, dealing with missing data poses a significant challenge for the intelligent traffic system (ITS). To address this issue, this study employs a nonconvex smoothly clipped absolute deviation (SCAD) penalty customized for tensors to surrogate tensor rank and incorporates the deep plug-and-play (PnP) prior into the low-rank tensor completion (LRTC) model. An efficient iterative framework is formulated to integrate these penalties into the alternating direction method of multipliers (ADMM) method. Moreover, two imputation methods, namely LRTC-SCAD and LRTC-SCAD-DeepPnP, are developed, affirming that the LRTC-SCAD method ensures convergence to the global optimum. We conduct simulated experiments using real-world traffic datasets, and our proposed methods outperform state-of-the-art imputation methods. For instance, on the Portland dataset, LRTC-SCAD achieves a noteworthy 9.86% improvement in mean absolute percentage error (MAPE) compared to the cutting-edge LRTC method while consuming only 28.26% of its total running time. Similarly, on the PeMS dataset, LRTC-SCAD-DeepPnP achieves an average 11.59% enhancement in MAPE, with visually compelling improvements in imputation results, further validating its efficacy in maintaining local consistency.