小波变换与高斯拟合在光谱重叠峰解析中的应用

Implementation of Spectral Overlap Resolution Based on Wavelet Transforms and Gaussian Fitting

利用小波变换对小波低频系数置零、高频系数阈值量化,实现了光谱信号的基线校正和谱线去噪;对光谱信号进行多尺度小波变换,搜寻各层小波系数模极值所构成的脊线,并对其中复合脊线进行校正,脊线中小波尺度参量最大时所对应的位置即为峰位;根据得到的峰位值,在最小二乘意义下寻找由多个单峰高斯函数叠加而成的最佳拟合光谱,得到谱峰峰强以及峰宽信息.利用该算法对含有基线漂移和随机噪声的光谱重叠峰进行解析,结果表明该算法能够较好地分离重叠峰,其中利用多尺度小波变换求解得到的峰位值偏差在±1.3以内,通过高斯拟合得到的峰强值偏差不超过8.5%.与现有算法求解得到的谱峰信息对比可知,本文所设计的光谱重叠峰解析算法具有一定优势.

Aiming at the problems of spectral overlap peaks, wavelet transforms was used, by setting the low-frequency wavelet coefficients to zero and thresholding the high-frequency coefficients, baseline-drift correction and spectral denoising were completed simultaneously. The ridge lines posed by modulus maxima of wavelet coefficients were searched by multi-scale wavelet transforms, and the composite ridge lines were correctted. The peak position was corresponding to the position of the maximum scale parameter in the wavelet ridge lines. According to the obtained peak values, the least squares rule was used to find out the best-fit spectra which was superimposed by multiple unimodal Gaussian functions, thus, the intensity and width information can be carried out. Finally, method was applied to resolve overlapping spectrum containing composite baseline-drift and random noise, the results showed that the algorithm can separate these overlapping peaks very well, the deviation of peak position calculated by multi-scale wavelet transforms was within~ 1.3, and the deviation of peak intensity fitted by Gaussian functions was no more than 8. 5%. Comparing with the peak information obtained by existing mature algorithm, to some extent, the proposed spectral overlap resolving algorithm is superior.