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Entropy 2010, 12(12), 2386-2396; doi:10.3390/e12122386
Article

Uncertainty Analysis of Decomposition Level Choice in Wavelet Threshold De-Noising

,
*  and
State Key Laboratory of Pollution Control and Resource Reuse, Department of Hydrosciences, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, China
* Author to whom correspondence should be addressed.
Received: 1 November 2010 / Revised: 16 November 2010 / Accepted: 29 November 2010 / Published: 30 November 2010
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Abstract

In this paper, the complexities of various noises, which are quantified by wavelet energy entropy (WEE) and differential coefficient of WEE (D(WEE)), were first analyzed and their uncertainties then estimated and described using confidence intervals. Then, quantitative criterion for judging the WEE and D(WEE) difference between noisy series and noise was put forward, based on which the decomposition level (DL) choice method in wavelet threshold de-noising proposed in 2010 by Sang et al. was improved. Finally, analytical results from examples verified the performance of the improved method, and also demonstrated its much wider applicability; moreover, the DL chosen using it is more reliable because of the fact that uncertainty is taken into consideration.
Keywords: time series analysis; uncertainty analysis; wavelet; decomposition level; noise; wavelet energy entropy; complexity time series analysis; uncertainty analysis; wavelet; decomposition level; noise; wavelet energy entropy; complexity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sang, Y.-F.; Wang, D.; Wu, J.-C. Uncertainty Analysis of Decomposition Level Choice in Wavelet Threshold De-Noising. Entropy 2010, 12, 2386-2396.

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