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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Published inMathematical problems in engineering Vol. 2019; no. 2019; pp. 1 - 14
Main Authors Daković, Miloš, Sejdić, Ervin, Stanković, Ljubiša
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2019
Hindawi
Hindawi Limited
Subjects
Frequency distribution
Graphical representations
Parameters
Signal analysis
Smoothness
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2019/3208569