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arXiv · 1512.00775

Uncertainty Principle and Sampling of Signals Defined on Graphs

Mikhail Tsitsvero·Sergio Barbarossa·Paolo Di Lorenzo
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Abstract

In many applications, from sensor to social networks, gene regulatory networks or big data, observations can be represented as a signal defined over the vertices of a graph. Building on the recently introduced Graph Fourier Transform, the first contribution of this paper is to provide an uncertainty principle for signals on graph. As a by-product of this theory, we show how to build a dictionary of maximally concentrated signals on vertex/frequency domains. Then, we establish a direct relation between uncertainty principle and sampling, which forms the basis for a sampling theorem of signals defined on graph. Based on this theory, we show that, besides sampling rate, the samples' location plays a key role in the performance of signal recovery algorithms. Hence, we suggest a few alternative sampling strategies and compare them with recently proposed methods.

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BibTeXRIS

Mikhail Tsitsvero, Sergio Barbarossa, Paolo Di Lorenzo. 2015-12-02. Uncertainty Principle and Sampling of Signals Defined on Graphs. https://arxiv.org/abs/1512.00775

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