Subsampling for Graph Power Spectrum Estimation

TL;DR

This paper demonstrates that the power spectrum of stationary graph signals can be accurately estimated from a small subset of vertices using simple least squares, with an efficient greedy algorithm for optimal subsampling design.

Contribution

It introduces a method for subsampling graph vertices to estimate the power spectrum without spectral priors and proposes a greedy algorithm for optimal subsampling scheme design.

Findings

Accurate power spectrum estimation from subsampled data.

A near-optimal greedy algorithm for subsampling scheme design.

Validation of the method on stationary graph signals.

Abstract

In this paper we focus on subsampling stationary random processes that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.