采用不同小波母函数的阈值去噪方法性能分析

以用于测定汽油辛烷值的红外吸收光谱分析为背景，评估采用小波去噪方法时各种小波和阈值组合的去噪能力。文章构造了一个理想的原始光谱信号，考虑到小波去噪后信噪比以及原始光谱信号保留率这两者之间的协调关系，基于信噪比(SNR)定义了一个评价去噪优劣的评估系数η，在此基础上采用三种小波族系(Symlets，Daubechies，Coiflet)、四种阈值选取方法(Rigrsure，Sqtwolog，Heursure和Manimaxi)和三种阈值重调方法(One，Sln，Mln)对理想原始光谱信号进行了基于小波变换的信号去噪处理实验，以评价各种小波函数和阈值选取及重调方法的优劣。通过一系列的试验表明，对于该类型的信号，在实验所考察的小波族系和阈值选取及重调方法的范围内，采用Daubechies9或Symlet7，11，14，15小波，Rigrsure阈值选取规则和Sln阈值重调方法，可以得到最优的去噪性能。

Performance Analysis of Threshold Denoising via Different Kinds of Mother Wavelets

An ideal spectrum signal prototype is constructed in this paper based on the infrared ray spectrum of octane levelmeasurement to evaluate the performances of wavelet based threshold denoising approaches via different combinations of mother wavelet functions and thresholds. A performance index eta is defined to assess the signal-to-noise ratios (SNR) of denoising results, inconsideration of the trade-off between the SNR and the distortion of the original signal after wavelet denoising. Three families of mother wavelets (Symlets, Daubechies and Coiflet), four threshold selection rules (Rigrsure, Sqtwolog, Heursure and Manimaxi), and three threshold rescaling methods (One, Sln and Mln) are tested in a series of experiments to estimate the functioning of those wavelets and thresholding parameters. Experimental results show that in the cases investigated in this paper, the best denoising performance is reached via the combinations of Daubechies9 or Symlet7, 11, 14, 15 wavelets, "Rigrsure" threshold selection rule, and "Sln" threshold rescaling method.