Reconstructing Graph Signals from Noisy Dynamical Samples

TL;DR

This paper explores how to optimally sample and reconstruct signals on graphs over time, especially when data is noisy, by deriving conditions and algorithms that improve accuracy over previous methods.

Contribution

It provides necessary and sufficient conditions for space-time sampling on graphs and introduces algorithms for sensor placement to minimize reconstruction error.

Findings

Derived conditions for graph signal reconstruction from noisy samples.

Developed algorithms for optimal sensor placement.

Outperformed existing methods in numerical experiments.

Abstract

We investigate the dynamical sampling space-time trade-off problem within a graph setting. Specifically, we derive necessary and sufficient conditions for space-time sampling that enable the reconstruction of an initial band-limited signal on a graph. Additionally, we develop and test numerical algorithms for approximating the optimal placement of sensors on the graph to minimize the mean squared error when recovering signals from time-space measurements corrupted by i.i.d.~additive noise. Our numerical experiments demonstrate that our approach outperforms previously proposed algorithms for related problems.