Robust Time-Varying Graph Signal Recovery Over Dynamic Topology

We propose a time-varying graph signal recovery method that estimates the true graph signal from an observation corrupted by missing values, outliers of unknown positions, and some random noise. Furthermore, we assume the underlying graph to be time-varying like the signals, which we integrate into our formulation for better performance. Conventional studies on time-varying graph signal recovery have been focusing on online estimation and graph learning under the assumption that entire dynamic graphs are unavailable. However, there are many practical situations where the underlying graphs can be observed or easily generated by simple algorithms like the k-nearest neighbor, especially when targeting physical sensing data, where the graphs can be defined to represent spatial correlations. To address such cases, in this paper, we tackle a dynamic graph Laplacian-based recovery problem on given dynamic graphs. To solve this, we formulate the recovery problem as a constrained convex optimization problem to estimate both the time-varying graph signal and the sparsely modeled outliers simultaneously. We integrate the graph dynamics into the formulation by exploiting the given dynamic graph. In such a manner, we succeed in separating the different types of corruption and achieving state-of-the-art recovery performance in both synthetic and real-world problem settings. We also conduct an extensive study to compare the contribution of vertex and temporal domain regularization on the recovery performance.