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Title: Smooth local subspace projection for nonlinear noise reduction

Abstract

Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Local 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 smooth orthogonal decomposition (SOD) of bundles of reconstructed short-time trajectory strands 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.

Authors:
 [1]
  1. Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, Rhode Island 02881 (United States)
Publication Date:
OSTI Identifier:
22251399
Resource Type:
Journal Article
Journal Name:
Chaos (Woodbury, N. Y.)
Additional Journal Information:
Journal Volume: 24; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DECOMPOSITION; FILTERS; NOISE; NONLINEAR PROBLEMS; SMOOTH MANIFOLDS; TRAJECTORIES

Citation Formats

Chelidze, David. Smooth local subspace projection for nonlinear noise reduction. United States: N. p., 2014. Web. doi:10.1063/1.4865754.
Chelidze, David. Smooth local subspace projection for nonlinear noise reduction. United States. https://doi.org/10.1063/1.4865754
Chelidze, David. 2014. "Smooth local subspace projection for nonlinear noise reduction". United States. https://doi.org/10.1063/1.4865754.
@article{osti_22251399,
title = {Smooth local subspace projection for nonlinear noise reduction},
author = {Chelidze, David},
abstractNote = {Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Local 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 smooth orthogonal decomposition (SOD) of bundles of reconstructed short-time trajectory strands 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.},
doi = {10.1063/1.4865754},
url = {https://www.osti.gov/biblio/22251399}, journal = {Chaos (Woodbury, N. Y.)},
issn = {1054-1500},
number = 1,
volume = 24,
place = {United States},
year = {Sat Mar 15 00:00:00 EDT 2014},
month = {Sat Mar 15 00:00:00 EDT 2014}
}