On the degrees of freedom of signals on graphs

By Mikhail Tsitsvero, Sergio Barbarossa. 2015

16 citations recorded by the source corpus.

Continuous-time signals are well known for not being perfectly localized in both time and frequency domains. Conversely, a signal defined over the vertices of a graph can be perfectly localized in both vertex and frequency domains. We derive the conditions ensuring the validity of this property and then, building on this theory, we provide the conditions for perfect reconstruction of a graph signal from its samples. Next, we provide a finite step algorithm for the reconstruction of a band-limited signal from its samples and then we show the effect of sampling a non perfectly band-limited signal and show how to select the bandwidth that minimizes the mean square reconstruction error.

Subfields: Applied Mathematics, Cognitive Neuroscience, Computational Mechanics, Graph Learning, Optimization & Training

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Citations in the corpus

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (2016, background): “The works of [34, 25, 26] redefined uncertainty principles on graphs and showed that while intuitive concepts may be lost, enhanced localization principles can be derived.”
Signals on Graphs: Uncertainty Principle and Sampling (2015, background): “Building on [12], one could also introduce a GFT for directed graphs based on the eigendecomposition of the modiﬁed Laplacian for directed graphs introduced in [12].”