Daubechies小波主成分回归法机理及算法研究

将小波变换与主成分回归相结合,提出一种新型多元校正算法---小波基主成分回归法。理论分析和仿真实验表明,该法可更有效地去除噪声,提取有用信息。将其用于氯霉素及甲硝唑实际药物体系分析,与主成分回归法(PCR)相比,得到的回收率总平均相对误差由1.70%下降到0.90%。此外,通过将统计判据和小波多尺度分析相结合,发展了一种新的因子数判定方法。理论和实验研究表明,该法比传统因子数判定法具有更高的可靠性。

Investigation of the mechanism and algorithm of principal component regression based on daubechies wavelet

In this paper, a new algorithm for multivariate calibration named principle component regression based on wavelet (PCRW) is proposed. The algorithm is constructed by integrating wavelet transform with principal component regression. The results of theoretical analysis and simulated experiments demonstrate that the new algorithm can more effectively filter off noise and extract useful information from the actual spectral data. Applying this method to the practical analysis of Chloramphenicolum and Metronidazok leads to a decrease in the average of mean relative error (MRE) from 1.70% obtained by PCR to 0.90% obtained by PCRW. Furthermore, by combining statistical criteria and multiscale analysis of wavelet, a new method for determining the number of principle components is developed. The theoretical and experimental investigations show that the new method is more reliable than conventional ones.