Time-Varying Graph Signal Recovery Using High-Order Smoothness and Adaptive Low-rankness

TL;DR

This paper introduces a novel method for recovering time-varying graph signals by combining high-order smoothness and adaptive low-rank regularization, improving accuracy in applications like climate and epidemic monitoring.

Contribution

It proposes a new recovery approach using high-order Sobolev smoothness and error-function weighted nuclear norm, along with two efficient algorithms with proven convergence.

Findings

Outperforms state-of-the-art methods in synthetic data experiments

Effective in real-world climate and epidemic datasets

Demonstrates robustness and improved accuracy in signal recovery

Abstract

Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the characteristics of the underlying signals, such as the smoothness of the signal over the graph domain and the low-rank structure of the spatial-temporal signal modeled in a matrix form. As one of the most popular options, the graph Laplacian is commonly adopted in designing graph regularizations for reconstructing signals defined on a graph from partially observed data. In this work, we propose a time-varying graph signal recovery method based on the high-order Sobolev smoothness and an error-function weighted nuclear norm regularization to enforce the low-rankness. Two efficient algorithms based on the alternating direction method of multipliers and iterative reweighting are proposed, and convergence of one algorithm is shown in detail. We conduct various numerical experiments on synthetic and real-world data sets to demonstrate the proposed method's effectiveness compared to the state-of-the-art in graph signal recovery.