基于多重小波变换与新阈值函数的去噪方法研究*

基于小波分析的特点，提出了一种对信号数据进行多重小波变换阈值去噪的方法。新的阈值函数的构造是在研究D.L.Donoho和I.M.Johnstone提出的小波阈值去噪方法的基础上完成的。与传统的软硬阈值函数相比，新阈值函数在整个定义域内统一定义，表达式简单易于计算，与软阈值函数一样具有连续性，而且是高阶可导的，便于进行各种数学处理，克服了硬阈值函数不连续、软阈值函数中估计小波系数与分解小波系数之间存在着恒定偏差的缺点。仿真实验结果表明，采用新的阈值函数的去噪效果在信噪比增益和最小均方误差意义上均优于传统的软

De-noising method based on multiple wavelet transform and novel thresholding function

:Based on the characteristics of wavelet analysis,proposed a novel de-nosing method which combined multiple wavelet transform with a new thresholding function.The presented novel thresholding function based on the wavelet shrinkage put forward by D.L.Donoho and I.M.Johnstone and had many advantages over traditional thresholding functions. Comparing with the traditional thresholding functions, it is simple in expression, as continuous as the soft-thresholding function, and has a high order derivative which makes some kinds of mathematical disposals convenient .It overcames the shortcoming of the discontinuous character in hard-thresholding function and solves the problem of the permanent bias in soft- thresholding function.Simulation results indicate that the proposed de-noising method gives better SNR gains and MSE performance.