一种新的小波阈值去噪算法及仿真

A New Wavelet Threshold Denoising Algorithm and Simulation

针对传统软、硬阈值函数和现有的大部分研究文献中所设计的阈值函数存在的缺陷,提出了一个新的阈值函数,该函数在整个小波域内(包括阈值点处)连续可导,且除阈值点外高阶可导,便于各种数学处理。另外可以通过参数调整来获得有效的阈值函数,从而达到比较理想的去噪效果。然后在以信噪比为主要评价标准的前提下提出了一种新的确定小波最优分解层数的自适应算法,该算法简单实用,可确定最优分解层数以达到最佳信噪比。最后,在MATLAB环境下进行了仿真实验,仿真结果表明,该算法能够获得比较好的去噪效果,具有广阔的应用前景。

Aiming at the flaws of traditional soft and hard threshold functions and most of the threshold functions in existing literature, a new threshold function is presented in this paper, which is continuous and derivable in the whole wavelet domain besides the threshold points and has higher-order derivatives except for the threshold points, and facilitates various mathematical processing. Additionally, it can adjust the parameters to get through effective threshold function, so as to achieve the ideal denoising result. Then a new adaptive algorithm to determine the optimal wavelet decomposition level is proposed on condition that the SNR is the main evaluation standards, which is simple and practical, and can determine the optimal decomposition level to achieve the best SNR. Finally, Simulation results under MATLAB environment prove that the algo- rithm can achieve good denoising effect and has broad application prospect.