An Unstructured Mesh Approach to Nonlinear Noise Reduction for Coupled Systems

TL;DR

This paper introduces an unstructured mesh approach using triangulations and Voronoi diagrams to enhance nonlinear noise reduction in coupled systems, improving accuracy and convergence over previous grid-based methods.

Contribution

It develops an unstructured mesh technique for nonlinear noise reduction that outperforms grid-based methods in accuracy and convergence, especially in low data density regions.

Findings

Achieves asymptotic statistical convergence with test data.

Reduces synthetic noise more effectively on experimental signals.

Improves signal reconstruction accuracy over grid-based methods.

Abstract

To address noise inherent in electronic data acquisition systems and real world sources, Araki et al. [Physica D: Nonlinear Phenomena, 417 (2021) 132819] demonstrated a grid based nonlinear technique to remove noise from a chaotic signal, leveraging a clean high-fidelity signal from the same dynamical system and ensemble averaging in multidimensional phase space. This method achieved denoising of a time-series data with 100% added noise but suffered in regions of low data density. To improve this grid-based method, here an unstructured mesh based on triangulations and Voronoi diagrams is used to accomplish the same task. The unstructured mesh more uniformly distributes data samples over mesh cells to improve the accuracy of the reconstructed signal. By empirically balancing bias and variance errors in selecting the number of unstructured cells as a function of the number of available samples, the method achieves asymptotic statistical convergence with known test data and reduces synthetic noise on experimental signals from Hall Effect Thrusters (HETs) with greater success than the original grid-based strategy.