Signal processing with a distribution of graph operators

TL;DR

This paper introduces a flexible signal processing framework for networks that relies on the distribution of graph operators rather than explicit topology, extending traditional graph signal processing methods.

Contribution

It develops a novel framework based on operator distributions, generalizing existing graph signal processing techniques to cases with unknown network topology.

Findings

Framework encompasses traditional graph signal processing as a special case

Includes Fourier transform, filtering, and sampling theory within the new framework

Applicable to networks with unknown or uncertain topology

Abstract

In this paper, we develop a signal processing framework of a network without explicit knowledge of the network topology. Instead, we make use of knowledge on the distribution of operators on the network. This makes the framework flexible and useful when accurate knowledge of graph topology is unavailable. Moreover, the usual graph signal processing is a special case of our framework by using the delta distribution. The main elements of the theory include Fourier transform, theory of filtering and sampling.