Observing and tracking bandlimited graph processes from sampled measurements

Highlights

• Observing and tracking a graph process is paramount for different applications.

• A novel theoretical approach is proposed for these tasks.

• Theoretical conditions on the minimum number of nodes to sample are necessary.

• A mean squared error analysis links the graph topology with the process.

• Strategies to sample the process are provided.

Abstract

A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.