A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrappingopen access
- Authors
- Lim, Munwon; Omitaomu, Olufemi A.; Bae, Suk Joo
- Issue Date
- Sep-2020
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Keywords
- Bootstrap aggregating; complex wavelet transform; data-denoising; step-down test; wavelet shrinkage
- Citation
- IEEE ACCESS, v.8, pp.174763 - 174772
- Indexed
- SCIE
SCOPUS
- Journal Title
- IEEE ACCESS
- Volume
- 8
- Start Page
- 174763
- End Page
- 174772
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/145135
- DOI
- 10.1109/ACCESS.2020.3025103
- ISSN
- 2169-3536
- 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.
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