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Entropy-Based Wavelet De-noising Method for Time Series Analysis
State Key Laboratory of Pollution Control and Resource Reuse, Department of Hydrosciences, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, China
China Water International Engineering Consulting Co. Ltd., Beijing 100053, China
Hydrology Bureau of Yellow River Conservancy Committee of Ministry of Water Resources, Zhengzhou 450001, China
* Author to whom correspondence should be addressed.
Received: 9 October 2009; Accepted: 11 December 2009 / Published: 22 December 2009
Abstract: The existence of noise has great influence on the real features of observed time series, thus noise reduction in time series data is a necessary and significant task in many practical applications. When using traditional de-noising methods, the results often cannot meet the practical needs due to their inherent shortcomings. In the present paper, first a set of key but difficult wavelet de-noising problems are discussed, and then by applying information entropy theories to the wavelet de-noising process, i.e., using the principle of maximum entropy (POME) to describe the random character of the noise and using wavelet energy entropy to describe the degrees of complexity of the main series in original series data, a new entropy-based wavelet de-noising method is proposed. Analysis results of both several different synthetic series and typical observed time series data have verified the performance of the new method. A comprehensive discussion of the results indicates that compared with traditional wavelet de-noising methods, the new proposed method is more effective and universal. Furthermore, because it uses information entropy theories to describe the obviously different characteristics of noises and the main series in the series data is observed first and then de-noised, the analysis process has a more reliable physical basis, and the results of the new proposed method are more reasonable and are the global optimum. Besides, the analysis process of the new proposed method is simple and is easy to implement, so it would be more applicable and useful in applied sciences and practical engineering works.
Keywords: time series analysis; de-noising; information entropy; wavelet transform; uncertainty
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MDPI and ACS Style
Sang, Y.-F.; Wang, D.; Wu, J.-C.; Zhu, Q.-P.; Wang, L. Entropy-Based Wavelet De-noising Method for Time Series Analysis. Entropy 2009, 11, 1123-1147.
Sang Y-F, Wang D, Wu J-C, Zhu Q-P, Wang L. Entropy-Based Wavelet De-noising Method for Time Series Analysis. Entropy. 2009; 11(4):1123-1147.
Sang, Yan-Fang; Wang, Dong; Wu, Ji-Chun; Zhu, Qing-Ping; Wang, Ling. 2009. "Entropy-Based Wavelet De-noising Method for Time Series Analysis." Entropy 11, no. 4: 1123-1147.