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A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping
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DOI：10.1109/ACCESS.2020.3025103.png)
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摘要
En 中文
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.
Keyword:
Bootstrap aggregating
complex wavelet transform
data-denoising
step-down test
wavelet shrinkage
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IF:
3.6
论文数:
9.8W
被引数:
29.4W
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