Smooth projective nonlinear noise reduction
Date of Original Version
Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Locally projective noise reduction is one of the most effective tools. It is based on proper orthogonal decomposition (POD), and works for both map-like and continuously sampled time series. However, POD only looks at geometrical or topological properties of data and does not take into account the temporal characteristics of time series. Here we present a new smooth projective noise reduction method. It uses bundles of locally reconstructed trajectory strands and their smooth orthogonal decomposition (SOD) to identify smooth local subspaces. Restricting trajectories to these subspaces imposes temporal smoothness on the filtered time series. It is shown that SOD-based noise reduction significantly outperforms the POD-based method for continuously sampled noisy time series. Copyright © 2013 by ASME.
Proceedings of the ASME Design Engineering Technical Conference
Chelidze, David. "Smooth projective nonlinear noise reduction." Proceedings of the ASME Design Engineering Technical Conference 8, (2013). doi:10.1115/DETC2013-12884.