Observing and tracking bandlimited graph processes from sampled measurements

Elvin Isufi; Paolo Banelli; Paolo Di Lorenzo; Geert Leus

doi:10.1016/j.sigpro.2020.107749

Observing and tracking bandlimited graph processes from sampled measurements

Elvin Isufi, Paolo Banelli, Paolo Di Lorenzo, Geert Leus

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.

Original language	English (US)
Pages (from-to)	107749
Journal	Signal Processing
Volume	177
DOIs	https://doi.org/10.1016/j.sigpro.2020.107749
State	Published - Aug 21 2020
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-14
Acknowledged KAUST grant number(s): OSR-2015-Sensors-2700
Acknowledgements: This work was supported in part by the KAUST-MIT-TUD-Caltech consortium grant OSR-2015-Sensors-2700 Ext. 2018. The work of P. Di Lorenzo was in part done at University of Perugia and was supported by the “Fondazione Cassa di Risparimio di Perugia”.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Signal Processing
Software
Computer Vision and Pattern Recognition
Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/j.sigpro.2020.107749

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title = "Observing and tracking bandlimited graph processes from sampled measurements",

abstract = "A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.",

author = "Elvin Isufi and Paolo Banelli and Lorenzo, {Paolo Di} and Geert Leus",

note = "KAUST Repository Item: Exported on 2022-06-14 Acknowledged KAUST grant number(s): OSR-2015-Sensors-2700 Acknowledgements: This work was supported in part by the KAUST-MIT-TUD-Caltech consortium grant OSR-2015-Sensors-2700 Ext. 2018. The work of P. Di Lorenzo was in part done at University of Perugia and was supported by the “Fondazione Cassa di Risparimio di Perugia”. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1016/j.sigpro.2020.107749",

language = "English (US)",

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AU - Isufi, Elvin

AU - Banelli, Paolo

AU - Lorenzo, Paolo Di

AU - Leus, Geert

N1 - KAUST Repository Item: Exported on 2022-06-14 Acknowledged KAUST grant number(s): OSR-2015-Sensors-2700 Acknowledgements: This work was supported in part by the KAUST-MIT-TUD-Caltech consortium grant OSR-2015-Sensors-2700 Ext. 2018. The work of P. Di Lorenzo was in part done at University of Perugia and was supported by the “Fondazione Cassa di Risparimio di Perugia”. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2020/8/21

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N2 - A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.

AB - A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.

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SP - 107749

JO - Signal Processing

JF - Signal Processing

ER -

Observing and tracking bandlimited graph processes from sampled measurements

Abstract

Bibliographical note

ASJC Scopus subject areas

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