连续可微阈值函数与尺度阈值的小波去噪  

Wavelet denoising based on continuous differentiable threshold function and scale threshold

作　　者：陈家益 战荫伟[2] 曹会英 吴兴达 李小飞[3] 

机构地区：[1]广东医科大学信息工程学院 [2]广东工业大学计算机学院 [3]长江大学信息与数学学院

出　　处：《电子测量与仪器学报》2018年第10期169-176,共8页Journal of Electronic Measurement and Instrumentation

基　　金：国家自然科学基金(61170320);广东省自然科学基金(2015A030310178);广州市科技计划项目(201604016034);广东省医学科研基金(B2018190);湛江市科技攻关计划项目(2017B01142);广东医科大学科研基金(M2016046)资助项目

摘　　要：为克服硬阈值、软阈值、半软阈值以及最新提出的阈值函数等小波去噪算法存在的诸多缺陷,提出了连续可微阈值函数与尺度阈值的小波去噪算法。改进阈值函数具有连续性、渐近性和高阶可微性等良好的数学特性,在保持原始有用信号的前提下,对噪声进行去除。另外,对目前最常用的通用阈值进行改进,根据噪声的强度随分解尺度的增加而减少的规律,在每个小波分解尺度上自适应地设置不同的尺度阈值,保护了幅值较小的原始信号的小波系数。仿真实验的结果显示,相对于现有的小波阈值去噪算法,所提出的算法的信噪比提高1.5 dB以上,均方根误差降低0.015以上。去噪实验的效果图以及实验数据证明,所提出的算法具有更好的去噪性能。In order to overcome the deficiencies of wavelet denoising algorithms of hard threshold, soft threshold, semi-soft threshold and newly proposed threshold function, the wavelet denoising based on continuous differentiable threshold function and scale threshold is proposed. The improved threshold function proposed in this paper has the good mathematical properties of continuity, asymptotic and high order differentials, which removes the noise without destroying the original useful signal. In addition, the universal threshold of most commonly used is improved, according to the rule that the noise intensity decreases with decomposition scale increasing, different scale thresholds are adaptively set at each wavelet decomposition scale, so as to protect the wavelet coefficients of the original signals with small amplitude. The results of simulation experiment show that compared to the existing wavelet threshold denoising algorithms, the signal to noise ratio(SNR) of the proposed method increases more than 1.5 dB, and RMSE decreases more than 0.015. The denoised images as well as experimental data prove that the proposed method has better denoising performance.

关 键 词：小波变换 小波基 小波阈值去噪 连续可微阈值函数 尺度阈值 

分 类 号：TN911.4[电子电信—通信与信息系统]