Filtering Random Graph Processes over Random Time-Varying Graphs

Elvin Isufi*, Andreas Loukas, Andrea Simonetto, Geert Leus

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

69 Citations (Scopus)
51 Downloads (Pure)


Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochasticity in both the graph topology and the signal itself. To bridge this gap, we examine the statistical behavior of the two key filter types, finite impulse response and autoregressive moving average graph filters, when operating on random time-varying graph signals (or random graph processes) over random time-varying graphs. Our analysis shows that 1) in expectation, the filters behave as the same deterministic filters operating on a deterministic graph, being the expected graph, having as input signal a deterministic signal, being the expected signal, and 2) there are meaningful upper bounds for the variance of the filter output. We conclude this paper by proposing two novel ways of exploiting randomness to improve (joint graph-time) noise cancellation, as well as to reduce the computational complexity of graph filtering. As demonstrated by numerical results, these methods outperform the disjoint average and denoise algorithm and yield a (up to) four times complexity reduction, with a very little difference from the optimal solution.

Original languageEnglish
Article number7931690
Pages (from-to)4406-4421
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number16
Publication statusPublished - 18 May 2017

Bibliographical note

Accepted Author Manuscript


  • graph filters
  • graph signal denoising
  • graph sparsification
  • random graph signals
  • random graphs
  • Signal processing on graphs


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