Zhu Meng-Hua, Liu Liang-Gang, Zheng Mei, Qi Dong-Xu, Zheng Cai-Mu
Space Exploration Laboratory, Macao University of Science and Technology, Macao, China.
Guang Pu Xue Yu Guang Pu Fen Xi. 2009 Oct;29(10):2721-4.
In the present paper, a new criterion is derived to obtain the optimum fitting curve while using Cubic B-spline basis functions to remove the statistical noise in the spectroscopic data. In this criterion, firstly, smoothed fitting curves using Cubic B-spline basis functions are selected with the increasing knot number. Then, the best fitting curves are selected according to the value of the minimum residual sum of squares (RSS) of two adjacent fitting curves. In the case of more than one best fitting curves, the authors use Reinsch's first condition to find a better one. The minimum residual sum of squares (RSS) of fitting curve with noisy data is not recommended as the criterion to determine the best fitting curve, because this value decreases to zero as the number of selected channels increases and the minimum value gives no smoothing effect. Compared with Reinsch's method, the derived criterion is simple and enables the smoothing conditions to be determined automatically without any initial input parameter. With the derived criterion, the satisfactory result was obtained for the experimental spectroscopic data to remove the statistical noise using Cubic B-spline basis functions.
在本文中，推导了一种新的准则，用于在使用三次B样条基函数去除光谱数据中的统计噪声时获得最优拟合曲线。在该准则中，首先，随着节点数增加，选择使用三次B样条基函数的平滑拟合曲线。然后，根据两条相邻拟合曲线的最小残差平方和（RSS）值选择最佳拟合曲线。在存在多条最佳拟合曲线的情况下，作者使用Reinsch的第一个条件来找到更好的曲线。不建议将带有噪声数据的拟合曲线的最小残差平方和（RSS）作为确定最佳拟合曲线的准则，因为随着所选通道数增加，该值会降至零，且最小值没有平滑效果。与Reinsch方法相比，推导的准则简单，无需任何初始输入参数就能自动确定平滑条件。使用推导的准则，在使用三次B样条基函数去除实验光谱数据中的统计噪声时获得了满意的结果。
