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...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2019-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2019/3208569 |
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. |
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ISSN: | 1024-123X 1563-5147 |