基于经验模态分解的改进乘性噪声去除方法  

Modified Signal De-noising Approach for Multiplicative Noise Based on Empirical Mode Decomposition

作　　者：焦卫东[1] 蒋永华[1] 林树森[1] 

机构地区：[1]浙江师范大学机械设备与测控技术研究所,金华321004

出　　处：《机械工程学报》2015年第24期1-8,共8页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51575497;51405449);浙江省杰青基金(R1100002)资助项目

摘　　要：乘性噪声往往由不理想的(时变的或非线性的)信道引起,它与信号是相乘的关系,因此难以消除。在乘性噪声消除应用背景下,引入同态变换去除噪声与信号的相倚性,将乘性噪声转化为加性噪声,并应用经验模态分解技术进一步研究受均匀分布白噪声污染的谐波信号及其同态变型的能量分布特性,据此建立起适用于乘性噪声去除的本征模函数幅值滤波新阈值准则。从而,形成基于经验模态分解的改进乘性噪声去除方法。结果表明,采用柔性阈值的改进算法对乘性噪声的去除效果最佳。而且,基于二阶多项式回归分析所构建的本征模函数幅值滤波阈值准则已经可以获得较高的源信号重建精度,过高的多项式阶次会导致本征模函数幅值滤波阈值与其实际噪声能量水平的失配,从而显著地降低算法的去噪性能。Multiplicative noise is usually caused by non-ideal（non-stationary or nonlinear） channel. The signal is multiplied by the noise in mixture model. Therefore, it is difficult to remove it. Under the background of multiplicative noise reduction, multiplicative noise can be converted into additive one, by introducing the well-known homomorphic transformation to remove the coupling between noise and signal. Characteristics of energy distribution of harmonic signal and its homomorphic version, disturbed by uniform white noise, are further studied using empirical mode decomposition（EMD）, which leads to one new amplitude-thresholding rule of intrinsic mode functions（IMFs）, adaptive to the application requirement of multiplicative noise reduction. Thus, modified EMD based signal de-noising approaches for multiplicative noise reduction are proposed. Experimental results show that the best de-noising performance is given by the modified algorithm with soft threshold, i.e. HEMDA-S. Furthermore, high reconstruction precision of source signal can be already assured by the modified de-noising algorithm, by using the constructed amplitude-thresholding rule of IMFs based on second-order polynomial regression analysis. The mismatch between the used amplitude-threshold on IMFs and their actual noise levels may occur if the order of used regression polynomial is too high, which will significantly reduce de-noising performance of the modified algorithm.

关 键 词：经验模态分解 本征模函数 幅值阈值滤波 乘性噪声去除 

分 类 号：TN911[电子电信—通信与信息系统]