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We propose a time-varying graph signal recovery method for estimating thetrue time-varying graph signal from observations that are corrupted by missingvalues, unknown position outliers, and some random noise. Most existing studieson time-varying graph signal recovery focus on online estimation and graphlearning based on the assumption that the entire dynamic graphs are notavailable, and robust recovery formulations and algorithms that fully exploitthe entire dynamically changing graph structure have not been well studied. Onthe other hand, there are many situations, especially when dealing withtimevarying data obtained from physical sensor networks, where the appropriatedynamic graphs can be easily generated using simple algorithms such ask-nearest neighbor by exploiting information on time-varying spatial sensorlocations. In this paper, we focus on such cases and formulate dynamic graphsignal recovery as a constrained convex optimization problem thatsimultaneously estimates both time-varying graph signals and sparsely modeledoutliers. In our formulation, we use two types of regularizations, time-varyinggraph Laplacian-based and temporal differencebased, and also separately modeledmissing values with known positions and unknown outliers, to achieve robustestimation from highly degraded data. In addition, an algorithm is developed toefficiently solve the optimization problem based on a primaldual splittingmethod. Extensive experiments on simulated drone remote sensing data and realsea surface temperature distribution data demonstrate the advantages of theproposed method over existing methods.

Robust Time-Varying Graph Signal Recovery for Dynamic Physical Sensor Network Data