Gabor-type frames for signal processing on graphs

TL;DR

This paper introduces a new framework for Gabor-type frames on graphs, providing sharp bounds and analyzing their behavior on Cayley graphs using group representation theory, advancing signal processing on networks.

Contribution

It proposes a flexible method for constructing Gabor frames on graphs with sharp bounds, extending previous approaches and analyzing their properties on Cayley graphs.

Findings

Sharp bounds for Gabor frames on graphs

Construction of translation operators for Cayley graphs

Impact of eigenbasis choice on frame properties

Abstract

In the past decade, significant progress has been made to generalize classical tools from Fourier analysis to analyze and process signals defined on networks. In this paper, we propose a new framework for constructing Gabor-type frames for signals on graphs. Our approach uses general and flexible families of linear operators acting as translations. Compared to previous work in the literature, our methods yield the sharp bounds for the associated frames, in a broad setting that generalizes several existing constructions. We also examine how Gabor-type frames behave for signals defined on Cayley graphs by exploiting the representation theory of the underlying group. We explore how natural classes of translations can be constructed for Cayley graphs, and how the choice of an eigenbasis can significantly impact the properties of the resulting translation operators and frames on the graph.