A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping

• Main Authors: Munwon Lim, Olufemi A. Omitaomu, Suk Joo Bae
• Format: Article
• Language: English
• Published: IEEE 2020-01-01
• Series: IEEE Access
• Subjects: Bootstrap aggregating; complex wavelet transform; data-denoising; step-down test; wavelet shrinkage
• Online Access: https://ieeexplore.ieee.org/document/9200482/

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.