In many applications of current interest, the observations are represented as a signal defined over a graph. The analysis of such signals requires the extension of standard signal processing tools. 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.

Uncertainty principle and sampling of signals defined on graphs / Tsitsvero, Mikhail; BARBAROSSA, Sergio; Di Lorenzo, Paolo. - ELETTRONICO. - 2016-February(2015), pp. 1813-1818. ((Intervento presentato al convegno 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015 tenutosi a Pacific Grove; United States [10.1109/ACSSC.2015.7421465].

Uncertainty principle and sampling of signals defined on graphs

BARBAROSSA, Sergio;Di Lorenzo, Paolo
2015

Abstract

In many applications of current interest, the observations are represented as a signal defined over a graph. The analysis of such signals requires the extension of standard signal processing tools. 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/960028
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