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.
Highlights
Graph signal processing (GSP) provides new tools to analyze signals on networks such as measurements in sensor networks, fMRI recordings in brain networks, and preferences in opinion networks [1]
The above works ignore the signal temporal evolution and focus on a single snapshot. This is limited because time varying graph signals, referred to as graph processes, are often encountered in practice, e.g., in consecutive sensor measurements, biological signal evolution prone to stimuli, and information diffusion over networks
We group the paper contributions into two parts. i) Observability of graph processes (Section 4): We develop a sampling theory to observe graph processes
Summary
Graph signal processing (GSP) provides new tools to analyze signals on networks such as measurements in sensor networks, fMRI recordings in brain networks, and preferences in opinion networks [1]. Preprint submitted to Elsevier bandlimited) in the graph frequency domain. This assumption is satisfied in temperature measurements in sensor networks [8], fMRI data in brain networks [12], and user ratings in recommendation networks [13], to name a few. The above works ignore the signal temporal evolution and focus on a single snapshot In our opinion, this is limited because time varying graph signals, referred to as graph processes, are often encountered in practice, e.g., in consecutive sensor measurements, biological signal evolution prone to stimuli, and information diffusion over networks. We highlight the differences with earlier works that dealt with graph processes
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