Abstract: This paper studies the advantages and disadvantages of hard threshold denoising and soft threshold denoising for wavelet denoising proposed by D.L.Donoho and I.M.Johnstone. And construct a new threshold function, it overcomes the point of discontinuity and soft threshold function derivative discontinuous shortcoming of the hard threshold processing method in[λ], but also the high order derivative, can retain big wavelet coefficient in the actual application, so as to preserve the signal as much, so to obtain better denoising effect. The simulation results show that, the new threshold function can effectively restrain the noise, the noise of the signal to noise ratio and root mean square error is better than soft and hard threshold function and several improved threshold function, has a high practical value.

Key words: wavelet, denoising, threshold function, Signal to Noise Ratio（SNR）

摘要： 对比研究了D.L.Donoho和I.M.Johnstone提出的小波阈值去噪的硬阈值去噪法和软阈值去噪法的优点和缺点，并在此基础上构造了一个新的阈值函数，它克服了硬阈值处理方法在[λ]点处不连续及软阈值函数导数不连续的缺点，而且是高阶可导的，在实际应用时能够保留较大的小波系数，从而保留了尽可能多的信号，进而能够获得更好的去噪效果。仿真实验结果显示，新阈值函数可有效地抑制噪声，其去噪后的信噪比和均方根误差均优于软硬阈值函数以及已有的几种改进阈值函数，具有较高的实用价值。

关键词: 小波, 去噪, 阈值函数, 信噪比