Graph Signal Sampling Under Stochastic Priors

TL;DR

This paper introduces a new sampling and recovery framework for stochastic graph signals characterized by GWSS, incorporating correction filters to improve reconstruction accuracy, applicable to various sampling methods and validated through experiments.

Contribution

It presents a generalized sampling framework with correction filters for GWSS graph signals, extending existing methods and enabling arbitrary sampling strategies.

Findings

Proposed correction filters reduce mean-squared error in signal reconstruction.

Framework applies to sampling in vertex or graph frequency domain.

Experimental results show improved MSE over existing approaches.

Abstract

We propose a generalized sampling framework for stochastic graph signals. Stochastic graph signals are characterized by graph wide sense stationarity (GWSS) which is an extension of wide sense stationarity (WSS) for standard time-domain signals. In this paper, graph signals are assumed to satisfy the GWSS conditions and we study their sampling as well as recovery procedures. In generalized sampling, a correction filter is inserted between sampling and reconstruction operators to compensate for non-ideal measurements. We propose a design method for the correction filters to reduce the mean-squared error (MSE) between original and reconstructed graph signals. We derive the correction filters for two cases: The reconstruction filter is arbitrarily chosen or predefined. The proposed framework allows for arbitrary sampling methods, i.e., sampling in the vertex or graph frequency domain. We also show that the graph spectral response of the resulting correction filter parallels that for generalized sampling for WSS signals if sampling is performed in the graph frequency domain. Furthermore, we reveal the theoretical connection between the proposed and existing correction filters. The effectiveness of our approach is validated via experiments by comparing its MSE with existing approaches.