An improved shift-invariant wavelet (S-I WT) de-noising algorithm based on LLS operator is proposed for high-resolution energy dispersive X-ray fluorescence. Sym8 is chosen as the wavelet basis function and performed noise reduction on the analog signal. Comparison of the de-noising effect of S-I WT, improved WT and LLS S-I WT (where LLS is the log square root operator) method are quantitatively evaluated by using evaluation criteria signal-to-noise-ratio (SNR), root mean square error and Pearson correlation coefficient. Meanwhile, a new evaluation criterion of de-noising effect, called peak area relative difference, is also proposed to evaluate the counting deviation. The results show that the LLS-SI WT is simple and reliable, can effectively reduce pseudo-Gibbs artificial signals and statistical fluctuation. Besides, this method simplifies the calculation, reduces the running time and improves the running efficiency. The LLS-SI WT is also applied to reduce the noise after adding strong noise to the signal, the SNR has been improved from 14.0040 to 14.7552, and most of the characteristic peak information retains to the greatest extent.

中文翻译：

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一种应用于EDXRF的基于LLS算子的SI WT去噪算法

针对高分辨率能量色散 X 射线荧光，提出了一种基于 LLS 算子的改进的平移不变小波 (SI WT) 去噪算法。选择Sym8作为小波基函数，对模拟信号进行降噪处理。SI WT、改进WT和LLS SI WT（其中LLS为对数平方根算子）方法的去噪效果比较采用评估标准信噪比（SNR）、均方根误差进行定量评估和皮尔逊相关系数。同时，还提出了一种新的去噪效果评价标准，称为峰面积相对差，用于评价计数偏差。结果表明，LLS-SI WT简单可靠，能有效减少伪吉布斯人工信号和统计波动。除了，该方法简化了计算，减少了运行时间，提高了运行效率。在信号中加入强噪声后，同样应用LLS-SI WT降噪，信噪比从14.0040提高到14.7552，最大程度保留了大部分特征峰信息。