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A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs
Xianwei Zheng1,2; Yuan Yan Tang2,3; Jiantao Zhou4,5
2019-02-01
Source PublicationIEEE Transactions on Signal Processing
ISSN1053-587X
Volume67Issue:7Pages:1696-1711
Abstract

The state-of-the-art graph wavelet decomposition was constructed by maximum spanning tree (MST)-based downsampling and two-channel graph wavelet filter banks. In this work, we first show that: 1) the existing MST-based downsampling could become unbalanced, i.e., the sampling rate is far from 1/2, which eventually leads to low representation efficiency of the wavelet decomposition; and 2) not only low-pass components, but also some high-pass ones can be decomposed to potentially achieve better decomposition performance. Based on these observations, we propose a new framework of adaptive multiscale graph wavelet decomposition for signals defined on undirected graphs. Specifically, our framework consists of two phases. Phase 1, called pre-processing, addresses the downsampling unbalance issues. We design maximal decomposition level estimation, unbalance detection, and unbalance reduction algorithms such that the downsampling rates of all levels are close to 1/2. Phase 2 concerns about adaptively finding low- or high-pass components that are worthy to be decomposed to improve the compactness of the decomposition. We suggest a graph signal Shannon-entropy-based adaptive decomposition algorithm. With applications on synthetic and real-world graph signals, we demonstrate that our framework provides better performance in terms of downsampling balance and signal compression, compared with other graph wavelet decomposition methods.

KeywordAdaptive Multiscale Decomposition Downsampling Unbalance Graph Signal Graph Signal Shannon Entropy Maximum Spanning Tree (Mst)
DOI10.1109/TSP.2019.2896246
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaEngineering
WOS SubjectEngineering, Electrical & Electronic
WOS IDWOS:000467063100019
Scopus ID2-s2.0-85061066738
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Cited Times [WOS]:6   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorJiantao Zhou
Affiliation1.School of Mathematics and Big Data,Foshan University,Foshan,528041,China
2.Department of Computer and Information Science,Faculty of Science and Technology,University of Macau,Macau,999078,China
3.Faculty of Science and Technology,UOW College Hong Kong,Community College of City University,Hong Kong
4.Department of Computer and Information Science, Faculty of Science and Technology
5.State Key Laboratory of Internet of Things for Smart City, University of Macau, Macau 999078, China
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology;  University of Macau
Recommended Citation
GB/T 7714
Xianwei Zheng,Yuan Yan Tang,Jiantao Zhou. A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs[J]. IEEE Transactions on Signal Processing,2019,67(7):1696-1711.
APA Xianwei Zheng,Yuan Yan Tang,&Jiantao Zhou.(2019).A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs.IEEE Transactions on Signal Processing,67(7),1696-1711.
MLA Xianwei Zheng,et al."A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs".IEEE Transactions on Signal Processing 67.7(2019):1696-1711.
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