On Critical Sampling of Time-Vertex Graph Signals

TL;DR

This paper investigates the optimal sampling and reconstruction of joint time-vertex graph signals, establishing conditions for minimal sampling and proposing an efficient algorithm for critical sampling set construction.

Contribution

It introduces a theoretical framework for critical sampling of joint time-vertex signals and provides an algorithm to construct minimal sampling sets based on this theory.

Findings

Existence of critical sampling sets proven

Necessary conditions for minimal sampling established

An efficient algorithm for constructing sampling sets proposed

Abstract

Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical sampling set using minimum number of samples in time and graph domain respectively. The theory proposed in this paper suggests to assign heterogeneous sampling pattern for each node in a network under the constraint of minimum resources. An efficient algorithm is also provided to construct a critical sampling set.