Local Smoothness of Graph Signals

Abstract EN

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.