On Sampling of Bandlimited Graph Signals

Mo Han; Jun Shi; Yiqiu Deng; Weibin Song

doi:10.1007/978-3-319-73447-7_62

On Sampling of Bandlimited Graph Signals

Mo Han
, Jun Shi^*
, Yiqiu Deng
, Weibin Song

^*Corresponding author for this work

School of Electronics and Information Engineering

Harbin Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

The signal processing on graphs has been widely used in various fields, including machine learning, classification and network signal processing, in which the sampling of bandlimited graph signals plays an important role. In this paper, we discuss the sampling of bandlimited graph signals based on the theory of function spaces, which is consistent with the pattern of the Shannon sampling theorem. First, we derive an interpolation operator by constructing bandlimited space of graph signals, and the corresponding sampling operator is also obtained. Based on the relationship between the interpolation and sampling operators, a sampling theorem for bandlimited graph signals is proposed, and its physical meaning in the graph frequency domain is also given. Furthermore, the implementation of the proposed theorem via matrix calculation is discussed.

Original language	English
Title of host publication	Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings
Editors	Bo Li, Xuemai Gu, Gongliang Liu
Publisher	Springer Verlag
Pages	577-584
Number of pages	8
ISBN (Print)	9783319734460
DOIs	https://doi.org/10.1007/978-3-319-73447-7_62
State	Published - 2018
Event	2nd International Conference on Machine Learning and Intelligent Communications, MLICOM 2017 - Weihai, China Duration: 5 Aug 2017 → 6 Aug 2017

Publication series

Name	Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST
Volume	227 LNICST
ISSN (Print)	1867-8211

Conference

Conference	2nd International Conference on Machine Learning and Intelligent Communications, MLICOM 2017
Country/Territory	China
City	Weihai
Period	5/08/17 → 6/08/17

Keywords

Graph signals
Sampling
Signal processing on graphs

Access to Document

10.1007/978-3-319-73447-7_62

Cite this

Han, M., Shi, J., Deng, Y., & Song, W. (2018). On Sampling of Bandlimited Graph Signals. In B. Li, X. Gu, & G. Liu (Eds.), Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings (pp. 577-584). (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST; Vol. 227 LNICST). Springer Verlag. https://doi.org/10.1007/978-3-319-73447-7_62

Han, Mo ; Shi, Jun ; Deng, Yiqiu et al. / On Sampling of Bandlimited Graph Signals. Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings. editor / Bo Li ; Xuemai Gu ; Gongliang Liu. Springer Verlag, 2018. pp. 577-584 (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST).

@inproceedings{3745b4bed679415ea09d690ef62040b2,

title = "On Sampling of Bandlimited Graph Signals",

abstract = "The signal processing on graphs has been widely used in various fields, including machine learning, classification and network signal processing, in which the sampling of bandlimited graph signals plays an important role. In this paper, we discuss the sampling of bandlimited graph signals based on the theory of function spaces, which is consistent with the pattern of the Shannon sampling theorem. First, we derive an interpolation operator by constructing bandlimited space of graph signals, and the corresponding sampling operator is also obtained. Based on the relationship between the interpolation and sampling operators, a sampling theorem for bandlimited graph signals is proposed, and its physical meaning in the graph frequency domain is also given. Furthermore, the implementation of the proposed theorem via matrix calculation is discussed.",

keywords = "Graph signals, Sampling, Signal processing on graphs",

author = "Mo Han and Jun Shi and Yiqiu Deng and Weibin Song",

note = "Publisher Copyright: {\textcopyright} 2018, ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering.; 2nd International Conference on Machine Learning and Intelligent Communications, MLICOM 2017 ; Conference date: 05-08-2017 Through 06-08-2017",

year = "2018",

doi = "10.1007/978-3-319-73447-7\_62",

language = "英语",

isbn = "9783319734460",

series = "Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST",

publisher = "Springer Verlag",

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editor = "Bo Li and Xuemai Gu and Gongliang Liu",

booktitle = "Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings",

address = "德国",

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Han, M, Shi, J, Deng, Y & Song, W 2018, On Sampling of Bandlimited Graph Signals. in B Li, X Gu & G Liu (eds), Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings. Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST, vol. 227 LNICST, Springer Verlag, pp. 577-584, 2nd International Conference on Machine Learning and Intelligent Communications, MLICOM 2017, Weihai, China, 5/08/17. https://doi.org/10.1007/978-3-319-73447-7_62

On Sampling of Bandlimited Graph Signals. / Han, Mo; Shi, Jun; Deng, Yiqiu et al.
Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings. ed. / Bo Li; Xuemai Gu; Gongliang Liu. Springer Verlag, 2018. p. 577-584 (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST; Vol. 227 LNICST).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On Sampling of Bandlimited Graph Signals

AU - Han, Mo

AU - Shi, Jun

AU - Deng, Yiqiu

AU - Song, Weibin

PY - 2018

Y1 - 2018

N2 - The signal processing on graphs has been widely used in various fields, including machine learning, classification and network signal processing, in which the sampling of bandlimited graph signals plays an important role. In this paper, we discuss the sampling of bandlimited graph signals based on the theory of function spaces, which is consistent with the pattern of the Shannon sampling theorem. First, we derive an interpolation operator by constructing bandlimited space of graph signals, and the corresponding sampling operator is also obtained. Based on the relationship between the interpolation and sampling operators, a sampling theorem for bandlimited graph signals is proposed, and its physical meaning in the graph frequency domain is also given. Furthermore, the implementation of the proposed theorem via matrix calculation is discussed.

AB - The signal processing on graphs has been widely used in various fields, including machine learning, classification and network signal processing, in which the sampling of bandlimited graph signals plays an important role. In this paper, we discuss the sampling of bandlimited graph signals based on the theory of function spaces, which is consistent with the pattern of the Shannon sampling theorem. First, we derive an interpolation operator by constructing bandlimited space of graph signals, and the corresponding sampling operator is also obtained. Based on the relationship between the interpolation and sampling operators, a sampling theorem for bandlimited graph signals is proposed, and its physical meaning in the graph frequency domain is also given. Furthermore, the implementation of the proposed theorem via matrix calculation is discussed.

KW - Graph signals

KW - Sampling

KW - Signal processing on graphs

UR - https://www.scopus.com/pages/publications/85045238160

U2 - 10.1007/978-3-319-73447-7_62

DO - 10.1007/978-3-319-73447-7_62

M3 - 会议稿件

AN - SCOPUS:85045238160

SN - 9783319734460

T3 - Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST

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EP - 584

BT - Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings

A2 - Li, Bo

A2 - Gu, Xuemai

A2 - Liu, Gongliang

PB - Springer Verlag

T2 - 2nd International Conference on Machine Learning and Intelligent Communications, MLICOM 2017

Y2 - 5 August 2017 through 6 August 2017

ER -

Han M, Shi J, Deng Y, Song W. On Sampling of Bandlimited Graph Signals. In Li B, Gu X, Liu G, editors, Machine Learning and Intelligent Communications - Second International Conference, MLICOM 2017, Proceedings. Springer Verlag. 2018. p. 577-584. (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, LNICST). doi: 10.1007/978-3-319-73447-7_62

On Sampling of Bandlimited Graph Signals

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