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A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping

Title
A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping
Author
배석주
Keywords
Bootstrap aggregating; complex wavelet transform; data-denoising; step-down test; wavelet shrinkage
Issue Date
2020-10
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Citation
IEEE ACCESS, v. 8, page. 174763-174772
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.
URI
https://ieeexplore.ieee.org/document/9200482https://repository.hanyang.ac.kr/handle/20.500.11754/171958
ISSN
2169-3536
DOI
10.1109/ACCESS.2020.3025103
Appears in Collections:
COLLEGE OF ENGINEERING[S](공과대학) > INDUSTRIAL ENGINEERING(산업공학과) > Articles
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