Denoising Nonlinear Time Series by Adaptive Filtering and Wavelet Shrinkage: A Comparison

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Time series measured in real world is often nonlinear, even chaotic. To effectively extract desired information from measured time series, it is important to preprocess data to reduce noise. In this Letter, we propose an adaptive denoising algorithm. Using chaotic Lorenz data and calculating root-mean-square-error, Lyapunov exponent, and correlation dimension, we show that our adaptive algorithm more effectively reduces noise in the chaotic Lorenz system than wavelet denoising with three different thresholding choices. We further analyze an electroencephalogram (EEG) signal in sleep apnea and show that the adaptive algorithm again more effectively reduces the Electrocardiogram (ECG) and other types of noise contaminated in EEG than wavelet approaches. </para>