# Reconstruction of Time-varying Graph Signals via Sobolev Smoothness

arXiv: https://arxiv.org/abs/2207.06439 · HTML: https://mlsanity.com/paper/2207.06439/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2022.

## Built on by (most cited first, 18 of 18)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [Time-varying Signals Recovery via Graph Neural Networks](https://mlsanity.com/paper/2302.11313/) (2023)
- [Multilinear Kernel Regression and Imputation via Manifold Learning](https://mlsanity.com/paper/2402.03648/) (2024)
- [LLM Online Spatial-temporal Signal Reconstruction Under Noise](https://mlsanity.com/paper/2411.15764/) (2024)
- [Spatiotemporal Imputation with Graph-Informed Flow Matching](https://mlsanity.com/paper/2606.06682/) (2026)
- [Learning Graph ARMA Processes from Time-Vertex Spectra](https://mlsanity.com/paper/2302.06887/) (2023)
- [Higher-order Sparse Convolutions in Graph Neural Networks](https://mlsanity.com/paper/2302.10505/) (2023)
- [Online Graph Filtering Over Expanding Graphs](https://mlsanity.com/paper/2409.07204/) (2024)
- [Graph Signal Adaptive Message Passing](https://mlsanity.com/paper/2410.17629/) (2024)
- [Higher-Order GNNs Meet Efficiency: Sparse Sobolev Graph Neural Networks](https://mlsanity.com/paper/2411.04570/) (2024)
- [Learning Time-Varying Graph Signals via Koopman](https://mlsanity.com/paper/2511.06493/) (2025)
- [Estimation of a Causal Directed Acyclic Graph Process using Non-Gaussianity](https://mlsanity.com/paper/2211.13800/) (2022)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [A Novel Unified Extended Matrix for Graph Signal Processing: Theory and Application](https://mlsanity.com/paper/2508.16633/) (2025)
- [Randomized Space-Time Sampling for Affine Graph Dynamical Systems](https://mlsanity.com/paper/2509.16818/) (2025)
- [FLFL: Federated Latent Factor Learning for Private Recovery of Spatio-Temporal Signals](https://mlsanity.com/paper/2606.23091/) (2026)
- [Graph-Spectral Flow Matching for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2609.36765/) (2026)

## Abstract (arXiv)

Graph Signal Processing (GSP) is an emerging research field that extends the concepts of digital signal processing to graphs. GSP has numerous applications in different areas such as sensor networks, machine learning, and image processing. The sampling and reconstruction of static graph signals have played a central role in GSP. However, many real-world graph signals are inherently time-varying and the smoothness of the temporal differences of such graph signals may be used as a prior assumption. In the current work, we assume that the temporal differences of graph signals are smooth, and we introduce a novel algorithm based on the extension of a Sobolev smoothness function for the reconstruction of time-varying graph signals from discrete samples. We explore some theoretical aspects of the convergence rate of our Time-varying Graph signal Reconstruction via Sobolev Smoothness (GraphTRSS) algorithm by studying the condition number of the Hessian associated with our optimization problem. Our algorithm has the advantage of converging faster than other methods that are based on Laplacian operators without requiring expensive eigenvalue decomposition or matrix inversions. The proposed GraphTRSS is evaluated on several datasets including two COVID-19 datasets and it has outperformed many existing state-of-the-art methods for time-varying graph signal reconstruction. GraphTRSS has also shown excellent performance on two environmental datasets for the recovery of particulate matter and sea surface temperature signals.