Observing and tracking bandlimited graph processes from sampled measurements

Elvin Isufi, Paolo Banelli, Paolo Di Lorenzo, Geert Leus

Research output: Contribution to journalArticleScientificpeer-review

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.

Original languageEnglish
Article number107749
Pages (from-to)1-13
Number of pages13
JournalSignal Processing
Volume177
DOIs
Publication statusPublished - 2020

Keywords

  • Graph processes
  • Graph signal processing
  • Kalman filtering
  • Observability
  • Sampling on graphs
  • Time varying graph signals

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