Design of Sampling Set for Bandlimited Graph Signal Estimation

TL;DR

This paper proposes a convex optimization-based method for selecting sampling sets in bandlimited graph signal estimation, enabling efficient reconstruction from partial noisy measurements.

Contribution

It formulates the sampling set selection as a convex optimization problem and introduces a probabilistic quantization approach for practical sampling allocation.

Findings

The method effectively estimates bandlimited graph signals from partial samples.

Convex relaxation improves sampling set selection efficiency.

Numerical experiments validate the approach's performance.

Abstract

It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard. We formularize the problem as the experimental design of a linear regression model if we allow multiple measurements on a single node. By relaxing it to a convex optimization problem, we get the proportion of sample for each node given the budget of total sample size. Then, we use a probabilistic quantization to get the number of each node to be sampled. Moreover, we analyze how the sample size influences whether our object function is well-defined by perturbation analysis. Finally, we demonstrate the performance of the proposed approach through various numerical experiments.