﻿ 小波阈值去噪算法在XRD图谱去噪中的应用 An Improved Wavelet Threshold Denoising Algorithm for Analysing Signals in the XRD Spectrum

Vol.04 No.03(2015), Article ID:15797,6 pages
10.12677/AAM.2015.43028

An Improved Wavelet Threshold Denoising Algorithm for Analysing Signals in the XRD Spectrum

Li Mu, Haihui Wang, Yuhao Zhang

School of Mathematics and Systems Science, Beihang University, Beijing

Received: Jul. 9th, 2015; accepted: Jul. 27th, 2015; published: Aug. 3rd, 2015

ABSTRACT

In this paper, a new threshold function is put forward, which is based on the introduced wavelet threshold function. The new threshold function not only has the advantage of traditional ones but also is continuous. Experiments show that the denoising algorithm based on the new wavelet threshold function can remove the noise in the XRD spectrum more effectively and is more beneficial for qualitative and quantitative analysis.

Keywords:Threshold Function, Denoising, XRD Spectrum

1. 引言

X射线衍射在研究金属和合金的晶体结构等方面具有广泛的应用，通过分析XRD图谱获得材料的成分，以及材料的内部原子或分子的结构等信息。但在XRD分析的信号脉冲和数据采集实验中，实验源干扰众多，存在噪声，在寻峰过程中出现假峰和丢失弱峰[1] ，对定性定量分析产生不利，因此需要对实验数据降噪处理。

2. 小波阈值去噪

(1) 信号小波分解：选择合适的小波基函数和分解层数，对含噪信号作小波分解，得到小波系数。

(2) 高频系数阈值化：选择合适的阈值，对高频系数进行阈值处理，得到新的小波系数。

(3) 重构信号：用低频系数和阈值化后的高频系数进行小波重构，得到估计信号，即去噪后的信号。

(1) 硬阈值函数

(2) 软阈值函数

3. 新阈值函数的构建

(1) 函数1

(2) 函数2

4. 仿真实验

Figure 1. Comparison of waves after denoising by three threshold functions

Figure 2. Comparison of SNR and MSE

Figure 3. The signal denoised by the three denoising algorithms

Table 1. Comparison of SNR and MSE

Table 2. Comparison of SNR and MSE

Figure 4. The denoised part of noisy signal

Figure 5. The lost signal details of the three denoising algorithms

5. 结论

An Improved Wavelet Threshold Denoising Algorithm for Analysing Signals in the XRD Spectrum[J]. 应用数学进展, 2015, 04(03): 224-229. http://dx.doi.org/10.12677/AAM.2015.43028

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