A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping

doi:https://doi.org/10.1109/access.2020.3025103

Title: A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping

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Abstract

Wavelet thresholding (or shrinkage) attempts to remove the noises existing in the signals while preserving inherent pattern characteristics in the reconstruction of true signals. For data-denoising purpose, we present a new wavelet thresholding procedure which employs the step-down testing idea of identifying active contrasts in unreplicated fractional factorial experiments. The proposed method employs bootstrapping methods to a step-down test for thresholding wavelet coefficients. By introducing the concept of a false discovery error rate in testing wavelet coefficients, we shrink the wavelet coefficients with p -values higher than the error rate. The error rate controls the expected proportion of wrongly accepted coefficients among chosen wavelet coefficients. Bootstrap samples are used to approximate the p -value for computational efficiency. We also present some guidelines for selecting the values of hyper-parameters which affect the performance in the step-down thresholding procedure. Based on some common testing signals and an air-conditioner sounds example, the comparison of our proposed procedure with other thresholding methods in the literature is performed. The analytical results show that the proposed procedure has a potential in data-denoising and data-reduction in a variety of signal reconstruction applications.

Authors:

^[1];

^[2];

^[1]

Hanyang University, Seoul (Korea)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Publication Date:: 2020-09-18

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1669751

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Journal Article: Accepted Manuscript

Journal Name:: IEEE Access

Additional Journal Information:: Journal Volume: 8; Journal Issue: N/A; Journal ID: ISSN 2169-3536

Publisher:: IEEE

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Bootstrap aggregating; complex wavelet transform; data-denoising; step-down test; wavelet shrinkage

Citation Formats


                    Lim, Munwon, Omitaomu, Olufemi A., and Bae, Suk Joo. A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping.  United States: N. p., 2020. 
        Web.  doi:10.1109/access.2020.3025103.

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                    Lim, Munwon, Omitaomu, Olufemi A., & Bae, Suk Joo. A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping.  United States.  https://doi.org/10.1109/access.2020.3025103

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                    Lim, Munwon, Omitaomu, Olufemi A., and Bae, Suk Joo. Fri .  
        "A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping".  United States.  https://doi.org/10.1109/access.2020.3025103.  https://www.osti.gov/servlets/purl/1669751.

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@article{osti_1669751,

  title        = {A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping},

  author       = {Lim, Munwon and Omitaomu, Olufemi A. and Bae, Suk Joo},

  abstractNote = {Wavelet thresholding (or shrinkage) attempts to remove the noises existing in the signals while preserving inherent pattern characteristics in the reconstruction of true signals. For data-denoising purpose, we present a new wavelet thresholding procedure which employs the step-down testing idea of identifying active contrasts in unreplicated fractional factorial experiments. The proposed method employs bootstrapping methods to a step-down test for thresholding wavelet coefficients. By introducing the concept of a false discovery error rate in testing wavelet coefficients, we shrink the wavelet coefficients with p -values higher than the error rate. The error rate controls the expected proportion of wrongly accepted coefficients among chosen wavelet coefficients. Bootstrap samples are used to approximate the p -value for computational efficiency. We also present some guidelines for selecting the values of hyper-parameters which affect the performance in the step-down thresholding procedure. Based on some common testing signals and an air-conditioner sounds example, the comparison of our proposed procedure with other thresholding methods in the literature is performed. The analytical results show that the proposed procedure has a potential in data-denoising and data-reduction in a variety of signal reconstruction applications.},

  doi          = {10.1109/access.2020.3025103},

  url          = {https://www.osti.gov/biblio/1669751},
  journal      = {IEEE Access},

  issn         = {2169-3536},

  number       = N/A,

  volume       = 8,

  place        = {United States},

  year         = {2020},

  month        = {9}

}

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