Sampling Theory for Graph Signals on Product Graphs

TL;DR

This paper develops a sampling theory for graph signals on product graphs, enabling efficient sampling and recovery of bandlimited signals by leveraging the structure of product graphs, which model complex multi-modal data.

Contribution

It introduces a novel framework that exploits product graph structures for improved sampling and recovery of bandlimited signals, reducing sample and computational complexity.

Findings

Achieves significant savings in sample complexity

Reduces computational complexity for signal recovery

Extends sampling theory to multi-modal data modeled by product graphs

Abstract

In this paper, we extend the sampling theory on graphs by constructing a framework that exploits the structure in product graphs for efficient sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs that are composed from smaller graph atoms; we motivate how this model is a flexible and useful way to model richer classes of data that can be multi-modal in nature. Previous works have established a sampling theory on graphs for bandlimited signals. Importantly, the framework achieves significant savings in both sample complexity and computational complexity