A Novel Scheme for Support Identification and Iterative Sampling of Bandlimited Graph Signals

TL;DR

This paper introduces an efficient iterative sampling method for bandlimited graph signals that guarantees exact recovery in noiseless cases, robust support identification with minimal samples, and demonstrates effectiveness through simulations.

Contribution

It presents a novel iterative sampling scheme for support identification and reconstruction of bandlimited graph signals, including support detection with minimal samples.

Findings

Exact signal recovery in noiseless scenarios

Reconstruction error bounds in noisy cases

Support identification with minimal samples

Abstract

We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction error. We propose an efficient iterative selection sampling approach and show that in the noiseless case the original signal is exactly recovered from the set of selected nodes. In the case of noisy measurements, a bound on the reconstruction error of the proposed algorithm is established. We further address the support identification of the bandlimited signal with unknown support and show that under a pragmatic sufficient condition, the proposed framework requires minimal number of samples to perfectly identify the support. The efficacy of the proposed methods are illustrated through numerical simulations on synthetic and real-world graphs.