Dynamical sampling with additive random noise
For researchers in signal processing and dynamical systems, this work extends dynamical sampling theory to noisy environments, though the results are incremental.
The paper analyzes the performance of dynamical sampling algorithms under additive random noise, demonstrating successful recovery of driving operators on synthetic and real data with integrated denoising techniques.
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.