Sampling and Reconstruction of Signals on Product Graphs

TL;DR

This paper introduces a method for efficiently sampling and reconstructing signals on large product graphs by exploiting their structure, with proven near-optimal sampling sets and practical applications in sensor networks, point clouds, and recommender systems.

Contribution

It proposes a novel sampling scheme for product graphs that leverages their structure and provides a low-complexity greedy algorithm with near-optimal guarantees.

Findings

Effective sampling of large-scale product graphs demonstrated.

Numerical experiments show accurate reconstruction in real datasets.

Method applicable to sensor networks, point clouds, and recommender systems.

Abstract

In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. The proposed scheme is particularly useful for processing signals on large-scale product graphs. The sampling sets are designed using a low-complexity greedy algorithm and can be proven to be near-optimal. To illustrate the developed theory, numerical experiments based on real datasets are provided for sampling 3D dynamic point clouds and for active learning in recommender systems.