光学学报, 2018, 38 (4): 0430005, 网络出版: 2018-07-10   

基于广义S变换和奇异值分解的近红外光谱去噪

De-Noising of Near Infrared Spectra Based on Generalized S Transform and Singular Value Decomposition
作者单位
1 湖南文理学院物理与电子科学学院, 湖南 常德 415000
2 湖南财政经济学院信息技术与管理学院, 湖南 长沙 410205
摘要
针对近红外光谱物质含量检测过程中噪声影响模型精度和稳定性的问题,引入广义S变换与奇异值分解(SVD)。利用广义S变换得到光谱数据的时频谱,并将二维时频谱系数矩阵作为SVD的Hankel矩阵求解奇异值,再采用k-均值聚类算法对奇异值序列进行分类计算,确定重构奇异值个数,对去噪后的数据矩阵进行广义S逆变换得到去噪后的光谱数据。给出组合方法的基本理论和具体实现过程,对仿真数据和谷朊粉导数光谱进行去噪,并与传统的9点平滑法和小波软阈值法的去噪结果进行比较。结果表明:所提方法克服了时域或频域单维滤波的局限性,且无需参考噪声数据和选择基函数,在谷朊粉导数光谱去噪中,只需采用两个奇异值就能实现较好的去噪效果,降低了滤波过程的复杂度。采用所提方法处理后,近红外光谱的分析精度和模型的稳健性优于9点平滑处理法和小波软阈值法。相比9点平滑法,所提方法的预测集的决定系数由0.9436增大为0.9985,预测均方根误差由0.0843减小为0.0406,明显提高了谷朊粉中水分含量定量检测的精度。
Abstract
In order to solve the problem of the influence of noise on model accuracy and stability in detecting materials content using near infrared spectra, we introduce the generalized S transform and singular value decomposition (SVD). Firstly, we use the generalized S transform to obtain time-frequency spectra of spectral data, and then use the two-dimensional time-frequency coefficient matrix as the Hankel matrix of SVD to solve singular values. Secondly, we use the k-means clustering algorithm to classify the singular value sequence and determine the reconstructed singular values. Finally, the de-noised coefficient matrix is transformed by the generalized S inversion to obtain de-noised spectral data. The basic theory and realization process of the combination method are given, and simulated data and the first derivative spectrum of wheat gluten are de-noised with the combination method. The results are compared with the traditional 9-point smoothing method and wavelet soft thresholding method. It is found that the proposed method overcomes the limitation of single dimension filtering (time domain or frequency domain), and does not need to reference noise data and select the base function. In the de-noising of wheat gluten derivative spectra, only 2 singular values are enough to achieve better de-noising effect, which reduces the complexity of the filtering process. The accuracy of the near infrared spectrum analysis and the robustness of the proposed model are better than those of the traditional 9-point smoothing method and the wavelet soft thresholding method. The predictive coefficient of the prediction set of the proposed method is 0.9985, which is larger than that of the 9-point smoothing method (0.9436). The root mean square error of the proposed method is 0.0406, which is smaller than that of the 9-point smoothing method (0.0843). The accuracy of quantitative detection of moisture content in wheat gluten is improved obviously.

蔡剑华, 肖永良, 黎小琴. 基于广义S变换和奇异值分解的近红外光谱去噪[J]. 光学学报, 2018, 38(4): 0430005. Jianhua Cai, Yongliang Xiao, Xiaoqin Li. De-Noising of Near Infrared Spectra Based on Generalized S Transform and Singular Value Decomposition[J]. Acta Optica Sinica, 2018, 38(4): 0430005.

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