Dynamical sampling with additive random noise

TL;DR

This paper analyzes the robustness of dynamical sampling algorithms in finite dimensions under additive noise, combining theoretical validation and practical testing with denoising techniques on synthetic and real data.

Contribution

It provides new theoretical insights and numerical validation for recovering operators in dynamical sampling affected by additive noise.

Findings

Algorithms are effective in noise mitigation.

Theoretical results confirm operator recovery.

Successful application on real data sets.

Abstract

Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and study the impact of additive noise. The algorithms are implemented and tested on synthetic and real data sets, and denoising techniques are integrated to mitigate the effect of the noise. We also develop theoretical and numerical results that validate the algorithm for recovering the driving operators, which are defined via a real symmetric convolution.