Local Smoothness of Graph Signals
Miloš Daković, Ljubiša Stanković, Ervin Sejdić · Mathematical Problems in Engineering · 2019
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.