A new wavelet thresholding function based on hyperbolic tangent function
type: Item
instance of: scholarly article
title: A new wavelet thresholding function based on hyperbolic tangent function
zbMATH Open document ID: 1395.94035
DOI: 10.1155/2015/528656
author: Can He
author: Jianchun Xing
author: Juelong Li
author: Qiliang Yang
author: Ronghao Wang
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Thresholding function is an important part of the wavelet threshold denoising method, which can influence the signal denoising effect significantly. However, some defects are present in the existing methods, such as function discontinuity, fixed bias, and parameters determined by trial and error. In order to solve these problems, a new wavelet thresholding function based on hyperbolic tangent function is proposed in this paper. Firstly, the basic properties of hyperbolic tangent function are analyzed. Then, a new thresholding function with a shape parameter is presented based on hyperbolic tangent function. The continuity, monotonicity, and high-order differentiability of the new function are theoretically proven. Finally, in order to determine the final form of the new function, a shape parameter optimization strategy based on artificial fish swarm algorithm is given in this paper. Mean square error is adopted to construct the objective function, and the optimal shape parameter is achieved by iterative search. At the end of the paper, a simulation experiment is provided to verify the effectiveness of the new function. In the experiment, two benchmark signals are used as test signals. Simulation results show that the proposed function can achieve better denoising effect than the classical hard and soft thresholding functions under different signal types and noise intensities.
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 6926579
Wikidata QID: Q59118872
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/528656
OpenAlex ID: W1637473734
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description: scientific article; zbMATH DE number 6926579