Entropy-based method of choosing the decomposition level in wavelet threshold de-noising.

*(English)*Zbl 1229.62125Summary: 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.

##### MSC:

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62B10 | Statistical aspects of information-theoretic topics |

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |

##### Keywords:

time series analysis; noise; wavelet transform; decomposition level; threshold; wavelet energy entropy; probability distribution
PDF
BibTeX
XML
Cite

\textit{Y.-F. Sang} et al., Entropy 12, No. 6, 1499--1513 (2010; Zbl 1229.62125)

Full Text:
DOI

**OpenURL**

##### References:

[1] | DOI: 10.1029/91WR02269 |

[2] | DOI: 10.1016/j.jhydrol.2009.01.001 |

[3] | DOI: 10.1016/j.advwatres.2009.07.004 |

[4] | DOI: 10.1016/j.jhydrol.2009.01.042 |

[5] | DOI: 10.1109/18.382009 · Zbl 0820.62002 |

[6] | Natarajan, Filtering random noise from deterministic signals via data compression, IEEE Trans. Signal Process. 43 pp 2595– (1995) |

[7] | DOI: 10.1006/jsvi.2000.3275 |

[8] | DOI: 10.1016/S0022-1694(01)00534-0 |

[9] | DOI: 10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2 |

[10] | Percival, Wavelet Methods for Time Series Analysis (2000) · Zbl 0963.62079 |

[11] | DOI: 10.1109/78.923292 · Zbl 1369.94408 |

[12] | DOI: 10.1109/LSP.2006.870355 |

[13] | DOI: 10.3390/e11041123 · Zbl 1179.94027 |

[14] | DOI: 10.1109/18.119732 · Zbl 0849.94005 |

[15] | Berger, Removing noise from music using local trigonometric bases and wavelet packets, J. Audio Eng. Soc. 42 pp 808– (1994) |

[16] | Lou, An approach based on simplified KLT and wavelet transform for enhancing speech degraded by non-stationary wideband noise, J. Sound Vib. 268 pp 717– (2003) |

[17] | DOI: 10.1016/j.bspc.2006.08.004 |

[18] | Chui, An Introduction to Wavelets, Vol. 1 (Wavelet Analysis and Its Applications) (1992) · Zbl 0925.42016 |

[19] | DOI: 10.1016/j.sigpro.2005.06.017 · Zbl 1163.94319 |

[20] | DOI: 10.1016/j.compstruc.2007.02.025 |

[21] | Box, Time Series Analysis, Forecasting and Control (1994) |

[22] | DOI: 10.1103/PhysRev.106.620 · Zbl 0084.43701 |

[23] | DOI: 10.1016/j.jhydrol.2005.04.003 |

[24] | Wang, Hydrology Wavelet Analysis (in Chinese) (2005) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.