Print Email Facebook Twitter Filtering Random Graph Processes over Random Time-Varying Graphs Title Filtering Random Graph Processes over Random Time-Varying Graphs Author Isufi, E. (TU Delft Signal Processing Systems) Loukas, A. (Swiss Federal Institute of Technology) Simonetto, A. (IBM Research Ireland) Leus, G.J.T. (TU Delft Signal Processing Systems) Date 2017-05-18 Abstract 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. Subject graph filtersgraph signal denoisinggraph sparsificationrandom graph signalsrandom graphsSignal processing on graphs To reference this document use: http://resolver.tudelft.nl/uuid:60b44e91-6dc3-4269-a673-1a8b4cb29d82 DOI https://doi.org/10.1109/TSP.2017.2706186 ISSN 1053-587X Source IEEE Transactions on Signal Processing, 65 (16), 4406-4421 Bibliographical note Accepted Author Manuscript Part of collection Institutional Repository Document type journal article Rights © 2017 E. Isufi, A. Loukas, A. Simonetto, G.J.T. Leus Files PDF 26110629.pdf 2.3 MB Close viewer /islandora/object/uuid:60b44e91-6dc3-4269-a673-1a8b4cb29d82/datastream/OBJ/view