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

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.

[1]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[2]  David Labat,et al.  Recent advances in wavelet analyses: Part 1. A review of concepts , 2005 .

[3]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[4]  S. Dunn,et al.  Using long-term data sets to understand transit times in contrasting headwater catchments , 2009 .

[5]  Mikio Tohyama,et al.  ESTIMATION OF SPEECH COMPONENTS BY ACF ANALYSIS IN A NOISY ENVIRONMENT , 2001 .

[6]  Nicholas A Alexander,et al.  Correcting data from an unknown accelerometer using recursive least squares and wavelet de-noising , 2007 .

[7]  George Kalliris,et al.  Novel wavelet domain Wiener filtering de-noising techniques: Application to bowel sounds captured by means of abdominal surface vibrations , 2006, Biomed. Signal Process. Control..

[8]  Dong Wang,et al.  Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising , 2010, Entropy.

[9]  A. R. Summers,et al.  A wavelet-based method for improving signal-to-noise ratio and contrast in MR images. , 2000, Magnetic resonance imaging.

[10]  Vijay P. Singh,et al.  Stochastic observation error and uncertainty in water quality evaluation , 2009 .

[11]  Dong Wang,et al.  Entropy-Based Wavelet De-noising Method for Time Series Analysis , 2009, Entropy.

[12]  Michael R. Chernick,et al.  Wavelet Methods for Time Series Analysis , 2001, Technometrics.

[13]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[14]  Maarten Jansen.  Minimum risk thresholds for data with heavy noise , 2006, IEEE Signal Processing Letters.

[15]  Slobodan P. Simonovic,et al.  Noise reduction in chaotic hydrologic time series: facts and doubts , 2002 .

[16]  Bettina Schaefli,et al.  What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology , 2007 .

[17]  Maxim J. Goldberg,et al.  Removing noise from music using local trigonometric bases and wavelet packets , 1994 .

[18]  Balas K. Natarajan.  Filtering random noise from deterministic signals via data compression , 1995, IEEE Trans. Signal Process..

[19]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[20]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[21]  Adhemar Bultheel,et al.  Asymptotic behavior of the minimum mean squared error threshold for noisy wavelet coefficients of piecewise smooth signals , 2001, IEEE Trans. Signal Process..

[22]  Dong Wang,et al.  The relation between periods’ identification and noises in hydrologic series data , 2009 .

[23]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[24]  Vittoria Bruni,et al.  Wavelet-based signal de-noising via simple singularities approximation , 2006, Signal Process..

[25]  T. Raveendra,et al.  De-noising and regularization in generalized NAH for turbomachinery acoustic noise source reconstruction , 2010 .