Subsampling of Correlated Graph Signals

TL;DR

This paper investigates how to efficiently sample and reconstruct correlated graph signals using a generative model, proposing algorithms for node selection and demonstrating near-perfect recovery on various graph types.

Contribution

It introduces a method for subsampling correlated graph signals based on a generative model, including a node selection algorithm and error-based sampling size determination.

Findings

Node subsampling is always feasible for signals from a generative model.

The proposed greedy algorithm effectively selects nodes for reconstruction.

Near-perfect signal recovery is achievable with the method on different graphs.

Abstract

Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based generative model. The question then arises whether measurements can be obtained on a few nodes and whether the correlation structure between the signals can be used to reconstruct the graph signal on the remaining nodes. We show that node subsampling is always possible for graph signals obtained through a generative model. Further, a method to determine the number of nodes to select is proposed based on the tolerable error. A correlation-based fast greedy algorithm is developed for selecting the nodes. Finally, we verify the proposed method on different deterministic and random graphs, and show that near-perfect reconstruction is possible with node subsampling.