Tight framelets on graphs for multiscale data analysis

Yu Guang Wang; Xiaosheng Zhuang

doi:10.1117/12.2528414

Tight framelets on graphs for multiscale data analysis

Yu Guang Wang
, Xiaosheng Zhuang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

13 Citations (Scopus)

Abstract

In this paper, we discuss the construction and applications of decimated tight framelets on graphs. Based on graph clustering algorithms, a coarse-grained chain of graphs can be constructed where a suitable orthonormal eigenpair can be deduced. Decimated tight framelets can then be constructed based on the orthonormal eigen-pair. Moreover, such tight framelets are associated with filter banks with which fast framelet transform algorithms can be realized. An explicit toy example of decimated tight framelets on a graph is provided.

Original language	English
Title of host publication	Wavelets and Sparsity XVIII
Editors	Dimitri Van De Ville, Manos Papadakis, Yue M. Lu
Publisher	SPIE
ISBN (Electronic)	9781510629707
ISBN (Print)	9781510629691
DOIs	https://doi.org/10.1117/12.2528414
Publication status	Published - Aug 2019
Event	Conference on Wavelets and Sparsity XVIII - San Diego, United States Duration: 13 Aug 2019 → 15 Aug 2019

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	11138
ISSN (Print)	0277-786X
ISSN (Electronic)	1996-756X

Conference

Conference	Conference on Wavelets and Sparsity XVIII
Place	United States
City	San Diego
Period	13/08/19 → 15/08/19

Research Keywords

coarse-grained chain
decimated framelets
fast algorithms
fast framelet transforms
filter banks
framelets on graphs
graph Laplacian
graph signal processing
spectral graph theory
Tight framelets

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10.1117/12.2528414

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@inproceedings{5dfdc55a2b17462d9651efd94db03012,

title = "Tight framelets on graphs for multiscale data analysis",

abstract = "In this paper, we discuss the construction and applications of decimated tight framelets on graphs. Based on graph clustering algorithms, a coarse-grained chain of graphs can be constructed where a suitable orthonormal eigenpair can be deduced. Decimated tight framelets can then be constructed based on the orthonormal eigen-pair. Moreover, such tight framelets are associated with filter banks with which fast framelet transform algorithms can be realized. An explicit toy example of decimated tight framelets on a graph is provided.",

keywords = "coarse-grained chain, decimated framelets, fast algorithms, fast framelet transforms, filter banks, framelets on graphs, graph Laplacian, graph signal processing, spectral graph theory, Tight framelets",

author = "Wang, \{Yu Guang\} and Xiaosheng Zhuang",

year = "2019",

month = aug,

doi = "10.1117/12.2528414",

language = "English",

isbn = "9781510629691",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

publisher = "SPIE",

editor = "Ville, \{Dimitri Van De\} and Manos Papadakis and Lu, \{Yue M.\}",

booktitle = "Wavelets and Sparsity XVIII",

address = "United States",

note = "Conference on Wavelets and Sparsity XVIII ; Conference date: 13-08-2019 Through 15-08-2019",

}

Wang, YG & Zhuang, X 2019, Tight framelets on graphs for multiscale data analysis. in DVD Ville, M Papadakis & YM Lu (eds), Wavelets and Sparsity XVIII., 111380B, Proceedings of SPIE - The International Society for Optical Engineering, vol. 11138, SPIE, Conference on Wavelets and Sparsity XVIII, San Diego, California, United States, 13/08/19. https://doi.org/10.1117/12.2528414

Tight framelets on graphs for multiscale data analysis. / Wang, Yu Guang; Zhuang, Xiaosheng.
Wavelets and Sparsity XVIII. ed. / Dimitri Van De Ville; Manos Papadakis; Yue M. Lu. SPIE, 2019. 111380B (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 11138).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Tight framelets on graphs for multiscale data analysis

AU - Wang, Yu Guang

AU - Zhuang, Xiaosheng

PY - 2019/8

Y1 - 2019/8

N2 - In this paper, we discuss the construction and applications of decimated tight framelets on graphs. Based on graph clustering algorithms, a coarse-grained chain of graphs can be constructed where a suitable orthonormal eigenpair can be deduced. Decimated tight framelets can then be constructed based on the orthonormal eigen-pair. Moreover, such tight framelets are associated with filter banks with which fast framelet transform algorithms can be realized. An explicit toy example of decimated tight framelets on a graph is provided.

AB - In this paper, we discuss the construction and applications of decimated tight framelets on graphs. Based on graph clustering algorithms, a coarse-grained chain of graphs can be constructed where a suitable orthonormal eigenpair can be deduced. Decimated tight framelets can then be constructed based on the orthonormal eigen-pair. Moreover, such tight framelets are associated with filter banks with which fast framelet transform algorithms can be realized. An explicit toy example of decimated tight framelets on a graph is provided.

KW - coarse-grained chain

KW - decimated framelets

KW - fast algorithms

KW - fast framelet transforms

KW - filter banks

KW - framelets on graphs

KW - graph Laplacian

KW - graph signal processing

KW - spectral graph theory

KW - Tight framelets

UR - https://www.scopus.com/pages/publications/85077113692

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85077113692&origin=recordpage

U2 - 10.1117/12.2528414

DO - 10.1117/12.2528414

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9781510629691

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Wavelets and Sparsity XVIII

A2 - Ville, Dimitri Van De

A2 - Papadakis, Manos

A2 - Lu, Yue M.

PB - SPIE

T2 - Conference on Wavelets and Sparsity XVIII

Y2 - 13 August 2019 through 15 August 2019

ER -

Tight framelets on graphs for multiscale data analysis

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GRF: Dual Framelets on Manifolds and Graphs with Applications in Multiscale Data Analysis

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Tight framelets on graphs for multiscale data analysis

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GRF: Dual Framelets on Manifolds and Graphs with Applications in Multiscale Data Analysis

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