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

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:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]
  1. Hanyang University, Seoul (Korea)
  2. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Publication Date:
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.
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
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.
@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}
}

Journal Article:
Free Publicly Available Full Text
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