Traffic Flow Imputation and Denoising via Graph Signal Smoothness Priors

Reliable traffic data are essential for intelligent transportation systems, yet real-world measurements are often degraded by missing readings and sensor noise resulting from failures, communication loss, or environmental factors. This paper presents a unified Graph Signal Processing (GSP) framework for traffic flow imputation and denoising based on Laplacian regularization. The road network is represented as a directed, weighted graph whose vertices correspond to sensors and whose edges capture spatial proximity and directional connectivity. Three weighting schemes are investigated: a standard Gaussian kernel, a self-tuning Gaussian kernel with locally adaptive bandwidth, and a correlation-aware hybrid kernel that integrates spatial distance with empirical temporal correlation. Two complementary estimators are developed—a harmonic interpolation model and a Tikhonov regularizer—that jointly perform data recovery and noise suppression through a convex fidelity–smoothness trade-of. Model validation on the PEMS-BAY dataset demonstrates that graph-based methods consistently outperform purely temporal baselines under both random and burst sensor outages. The self-tuning and hybrid kernels achieve up to 25% lower mean absolute error, while the graph-Tikhonov model attains the lowest root mean square error (RMSE) and positive signal-to-noise ratio gains in denoising tasks. Overall, the proposed GSP framework provides an interpretable and computationally efficient approach for reliable traffic data reconstruction across large-scale spatio–temporal sensor networks.