  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.
