摘要
阈值函数选择和分解尺度确定是基于阈值的小波域非线性滤波的两个关键步骤。针对加性白噪声的情况,通过研究小波阈值去噪原理,得出了重构信号信噪比随分解尺度的单增变化规律,构造了用于指示最优分解尺度的目标函数;在分析白噪声小波系数高斯分布特性的基础上,提出了一种基于概率理论的阈值函数,通过极小化广义阈值估计偏差函数,得到了该阈值函数中参数的最优分布区间。仿真结果表明,构造的目标函数能够准确指示信号分解的最优尺度,广泛适用于硬阈值类函数;新阈值函数与另外两种改进型阈值函数相比,在信噪比意义下表现出一定的优越性。
The selection of threshold function and determination of decomposition level are two key steps in threshold-based nonlinear filtering by wavelet transform. In the presence of additive white noise, the variation rule of reconstructed signal SNR is concluded via research into the theory of wavelet threshold de-noising, and a target function is accordingly built to indicate the optimal decomposition level. Based on analysis of white noise wavelet coefficients distribution characteristic, a novel threshold function is built consequently. The optimal distribution area of a parameter in the threshold function is found by minimizing a generalized estimation error function. Simulation results indicate that optimal decomposition levels in threshold based denoising method could be determined precisely by the target function, which could be also applied to threshold functions similar to hard threshold function. Compared to other improved threshold functions, the novel threshold function outperforms the other two functions in the matter of SNR.
出处
《高电压技术》
EI
CAS
CSCD
北大核心
2009年第3期501-508,共8页
High Voltage Engineering
关键词
静态提升小波变换
sym4小波
阈值去噪
阈值函数
分解尺度
概率理论
stationary lifting wavelet
sym4 wavelet
threshold de-noising
threshold function
decomposition level
probability theory
作者简介
张弦1982-，男，博士生研究方向为支持向量机、小波理论及在信号处理中的应用电话：（029）84741538 Email：allaqe@163．com
王宏力1965-，男，博士，教授，博导研究方向为容错控制与智能诊断
