Isufi, Elvin
Loukas, Andreas
Simonetto, Andrea
Leus, Geert
Filtering Random Graph Processes Over Random Time-Varying Graphs
Ieee Transactions On Signal Processing
Ieee Transactions On Signal Processing
Ieee Transactions On Signal Processing
Ieee Transactions On Signal Processing
16
65
16
Signal processing on graphs
graph filters
random graphs
random graph signals
graph signal denoising
graph sparsification
2017
2017
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.
Institute of Electrical and Electronics Engineers
1053-587X
Ieee Transactions On Signal Processing
Journal Articles
10.1109/Tsp.2017.2706186