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A New Wavelet Thresholding Function Based on Hyperbolic Tangent Function

机译：基于双曲正切函数的新小波阈值函数

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摘要

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.
机译：阈值函数是小波阈值去噪方法的重要组成部分，它可以显着影响信号的去噪效果。但是，现有方法中存在一些缺陷，例如功能不连续性，固定偏差以及通过反复试验确定的参数。为了解决这些问题，本文提出了一种基于双曲正切函数的小波阈值函数。首先，分析了双曲正切函数的基本性质。然后，基于双曲正切函数，提出了具有形状参数的新阈值函数。理论上证明了新函数的连续性，单调性和高阶可微性。最后，为确定新函数的最终形式，提出了一种基于人工鱼群算法的形状参数优化策略。采用均方误差构造目标函数，并通过迭代搜索获得最佳形状参数。在本文的最后，提供了一个仿真实验来验证新功能的有效性。在实验中，将两个基准信号用作测试信号。仿真结果表明，在不同的信号类型和噪声强度下，该函数比经典的硬阈值和软阈值函数具有更好的去噪效果。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第16期|528656.1-528656.10|共10页
  • 作者

    He Can; Xing Jianchun; Li Juelong; Yang Qiliang; Wang Ronghao;

  • 作者单位

    PLA Univ Sci & Technol, Coll Def Engn, Nanjing 210007, Jiangsu, Peoples R China.;

    PLA Univ Sci & Technol, Coll Def Engn, Nanjing 210007, Jiangsu, Peoples R China.;

    Naval Def Engn, Tech Management Off, Beijing 100841, Peoples R China.;

    PLA Univ Sci & Technol, Coll Def Engn, Nanjing 210007, Jiangsu, Peoples R China.;

    PLA Univ Sci & Technol, Coll Def Engn, Nanjing 210007, Jiangsu, Peoples R China.;

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