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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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2019/3208569 |
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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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1725852328798453760 |