# Sampling Theory of Jointly Bandlimited Time-vertex Graph Signals

## TL;DR

This paper establishes theoretical bounds and practical sampling methods for reconstructing time-vertex graph signals that are bandlimited in joint spectral domain, applicable to various signal types and real datasets.

## Contribution

It introduces bounds on sampling density for jointly bandlimited TVGS and proposes reconstruction procedures for different signal types.

## Key findings

- Lower bounds on sampling density depend on spectral support measure.
- Sampling and reconstruction procedures are effective for various TVGS types.
- Proposed schemes work on real datasets.

## Abstract

Time-vertex graph signal (TVGS) models describe time-varying data with irregular structures. The bandlimitedness in the joint time-vertex Fourier spectral domain reflects smoothness in both temporal and graph topology. In this paper, we study the critical sampling of three types of TVGS including continuous-time signals, infinite-length sequences, and finite-length sequences in the time domain for each vertex on the graph. For a jointly bandlimited TVGS, we prove a lower bound on sampling density or sampling ratio, which depends on the measure of the spectral support in the joint time-vertex Fourier spectral domain. We also provide a lower bound on the sampling density or sampling ratio of each vertex on sampling sets for perfect recovery. To demonstrate that critical sampling is achievable, we propose the sampling and reconstruction procedures for the different types of TVGS. Finally, we show how the proposed sampling schemes can be applied to numerical as well as real datasets.