Sampling of graph signals via randomized local aggregations

TL;DR

This paper introduces a novel graph signal sampling method combining localized sampling with compressed sensing, providing theoretical guarantees for reconstruction without prior knowledge of the signal support.

Contribution

It proposes a new randomized local aggregation sampling technique that works universally for any graph and basis, without needing support or sparsity prior.

Findings

Provides theoretical guarantees for reconstruction and noise stability

Works for any graph and orthonormal basis

Does not require prior knowledge of signal support

Abstract

Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges arise and defining an efficient sampling strategy is not straightforward. Recently, several works have addressed this problem. The most common techniques select a subset of nodes to reconstruct the entire signal. However, such methods often require the knowledge of the signal support and the computation of the sparsity basis before sampling. Instead, in this paper we propose a new approach to this issue. We introduce a novel technique that combines localized sampling with compressed sensing. We first choose a subset of nodes and then, for each node of the subset, we compute random linear combinations of signal coefficients localized at the node itself and its neighborhood. The proposed method provides theoretical guarantees in terms of reconstruction and stability to noise for any graph and any orthonormal basis, even when the support is not known.