Local Smoothness of Graph Signals

Local Smoothness of Graph Signals

Analysis of vertex-varying spectral content of signals on graphs challenges the assumption of vertex invariance and requires the introduction of vertex-frequency representations as a new tool for graph signal analysis. Local smoothness, an important parameter of vertex-varying graph signals, is intr...

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Main Authors: Miloš Daković, Ljubiša Stanković, Ervin Sejdić
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/3208569
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spelling doaj-959a0a0fc54f4e13b3595b51bffeea082020-11-24T21:58:21ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/32085693208569Local Smoothness of Graph SignalsMiloš Daković0Ljubiša Stanković1Ervin Sejdić2University of Montenegro, Podgorica, MontenegroUniversity of Montenegro, Podgorica, MontenegroUniversity of Pittsburgh, Pittsburgh, PA, USAAnalysis of vertex-varying spectral content of signals on graphs challenges the assumption of vertex invariance and requires the introduction of vertex-frequency representations as a new tool for graph signal analysis. Local smoothness, an important parameter of vertex-varying graph signals, is introduced and defined in this paper. Basic properties of this parameter are given. By using the local smoothness, an ideal vertex-frequency distribution is introduced. The local smoothness estimation is performed based on several forms of the vertex-frequency distributions, including the graph spectrogram, the graph Rihaczek distribution, and a vertex-frequency distribution with reduced interferences. The presented theory is illustrated through numerical examples.http://dx.doi.org/10.1155/2019/3208569
collection DOAJ
language English
format Article
sources DOAJ
author Miloš Daković
Ljubiša Stanković
Ervin Sejdić
spellingShingle Miloš Daković
Ljubiša Stanković
Ervin Sejdić
Local Smoothness of Graph Signals
Mathematical Problems in Engineering
author_facet Miloš Daković
Ljubiša Stanković
Ervin Sejdić
author_sort Miloš Daković
title Local Smoothness of Graph Signals
title_short Local Smoothness of Graph Signals
title_full Local Smoothness of Graph Signals
title_fullStr Local Smoothness of Graph Signals
title_full_unstemmed Local Smoothness of Graph Signals
title_sort local smoothness of graph signals
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description Analysis of vertex-varying spectral content of signals on graphs challenges the assumption of vertex invariance and requires the introduction of vertex-frequency representations as a new tool for graph signal analysis. Local smoothness, an important parameter of vertex-varying graph signals, is introduced and defined in this paper. Basic properties of this parameter are given. By using the local smoothness, an ideal vertex-frequency distribution is introduced. The local smoothness estimation is performed based on several forms of the vertex-frequency distributions, including the graph spectrogram, the graph Rihaczek distribution, and a vertex-frequency distribution with reduced interferences. The presented theory is illustrated through numerical examples.
url http://dx.doi.org/10.1155/2019/3208569
work_keys_str_mv AT milosdakovic localsmoothnessofgraphsignals
AT ljubisastankovic localsmoothnessofgraphsignals
AT ervinsejdic localsmoothnessofgraphsignals
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