# Subset Random Sampling and Reconstruction of Finite Time-Vertex Graph Signals

## TL;DR

This paper introduces a subset random sampling method for finite time-vertex graph signals with unknown spectral support, along with a reconstruction framework that leverages low-rank, sparsity, and smoothness priors, validated through experiments.

## Contribution

It proposes a practical subset sampling scheme and a novel reconstruction framework for FTVGS with unknown spectral support, addressing real-world sampling constraints.

## Key findings

- High-probability reconstruction guarantees under certain conditions
- Effective reconstruction demonstrated through experiments
- Framework leveraging low-rank, sparsity, and smoothness priors

## Abstract

Finite time-vertex graph signals (FTVGS) provide an efficient representation for capturing spatio-temporal correlations across multiple data sources on irregular structures. Although sampling and reconstruction of FTVGS with known spectral support have been extensively studied, the case of unknown spectral support requires further investigation. Existing random sampling methods may extract samples from any vertex at any time, but such strategies are not friendly in practice, where sampling is typically limited to a subset of vertices and moments. To address this requirement, we propose a subset random sampling scheme for FTVGS. Specifically, we first randomly select a subset of rows and columns to form a submatrix, followed by random sampling within that submatrix. In theory, we provide sufficient conditions for reconstructing the original FTVGS with high probability. Additionally, we introduce a reconstruction framework incorporating low-rank, sparsity, and smoothness priors (LSSP), and verify the feasibility of the reconstruction and the effectiveness of the framework through experiments.