Bayesian Design of Sampling Set for Bandlimited Graph Signals

TL;DR

This paper introduces a Bayesian optimization framework for designing sampling sets in bandlimited graph signals, leveraging stochastic priors to improve estimation accuracy and proposing a heuristic algorithm for practical implementation.

Contribution

It presents a novel Bayesian approach to sampling set design for graph signals, incorporating prior knowledge and analyzing error metrics to enhance performance.

Findings

Bayesian DoS improves estimation accuracy over non-Bayesian methods.

Analysis of Gershgorin discs reveals how sampling choices affect error.

Proposed heuristic algorithm offers a practical solution without complex optimization.

Abstract

The design of sampling set (DoS) for bandlimited graph signals (GS) has been extensively studied in recent years, but few of them exploit the benefits of the stochastic prior of GS. In this work, we introduce the optimization framework for Bayesian DoS of bandlimited GS. We also illustrate how the choice of different sampling sets affects the estimation error and how the prior knowledge influences the result of DoS compared with the non-Bayesian DoS by the aid of analyzing Gershgorin discs of error metric matrix. Finally, based on our analysis, we propose a heuristic algorithm for DoS to avoid solving the optimization problem directly.