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Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising
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: 10 April 2010; Accepted: 27 May 2010 / Published: 10 June 2010
Abstract: In this paper, the energy distributions of various noises following normal, log-normal and Pearson-III distributions are first described quantitatively using the wavelet energy entropy (WEE), and the results are compared and discussed. Then, on the basis of these analytic results, a method for use in choosing the decomposition level (DL) in wavelet threshold de-noising (WTD) is put forward. Finally, the performance of the proposed method is verified by analysis of both synthetic and observed series. Analytic results indicate that the proposed method is easy to operate and suitable for various signals. Moreover, contrary to traditional white noise testing which depends on “autocorrelations”, the proposed method uses energy distributions to distinguish real signals and noise in noisy series, therefore the chosen DL is reliable, and the WTD results of time series can be improved.
Keywords: time series analysis; noise; wavelet transform; decomposition level; threshold; wavelet energy entropy; probability distribution
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MDPI and ACS Style
Sang, Y.-F.; Wang, D.; Wu, J.-C. Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising. Entropy 2010, 12, 1499-1513.
Sang Y-F, Wang D, Wu J-C. Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising. Entropy. 2010; 12(6):1499-1513.
Sang, Yan-Fang; Wang, Dong; Wu, Ji-Chun. 2010. "Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising." Entropy 12, no. 6: 1499-1513.