量子电子学报, 2008, 25 (1): 0025, 网络出版: 2010-06-07
小波变换中基于正交多项式拟合的边界延拓
A boundary prolongation method based on orthogonal polynomial fitting in wavelet transform
图像处理 小波变换 边界效应 正交多项式拟合 基线校正 image processing wavelet transform signal-end effect orthogonal polynomial fitting baseline correction
摘要
为消除小波分解过程中的边界效应,给出了一种基于多项式拟合的边界延拓的新方式。该延拓方式首先对信号边界处的N个点进行M阶正交多项式拟合,将信号在边界处的低频变化规律用正交多项式表示出来,再利用得到的边界处的低频变化规律对信号进行延拓,从而减少了边界处引入的突变量。研究表明,N取30~50、M取2~4较为合适。进一步的实验表明,利用小波变换在该延拓方式下对信号进行基线校正时,边界效应得到了明显的改善。
Abstract
A new boundary prolongation method based on orthogonal polynomial fitting was developed to remove the signal-end effect. In the prolongation method M-order orthogonal polynomial was fitted with N points for both ends firstly,the low-frequency function of signal's both ends was expressed by orthogonal polynomial,and then the signal was extended with function,so the imported high-frequency parts were lowered. Results showed that choosing N from 30~50 and M from 2~4 was proper. Further experiment showed that the signal-end effect was cut down clearly when the method mentioned above was used in baseline correction with wavelet transformation.
孔超, 方勇华, 兰天鸽, 熊伟, 董大明, 李大成. 小波变换中基于正交多项式拟合的边界延拓[J]. 量子电子学报, 2008, 25(1): 0025. KONG Chao, FANG Yong-hua, LAN Tian-ge, XIONG Wei, DONG Da-ming, LI Da-cheng. A boundary prolongation method based on orthogonal polynomial fitting in wavelet transform[J]. Chinese Journal of Quantum Electronics, 2008, 25(1): 0025.