一种基于几何含义的B样条小波分解重构简易算法

A simple algorithm for B-spline wavelet decomposition and reconstruction based on geometrical meanings

由于B样条基函数及其对应的小波不具有平移正交性,因而不能用现有的Mallat快速算法进行小波变换。文中在分析B样条小波分解重构思想的基础上,着重研究了B样条基函数在不同尺度下伸缩平移系之间的内在联系,用清晰的几何含义描述了重构矩阵的求解过程。该算法概念清晰,计算简单,结果稳定。最后用该算法给出了一条复杂曲线分解重构的实例。

On account of the B-spline basic function and its corresponding wavelets have no translational orthogonality; therefore it is impossible to carrying out wavelet transformation by the use of the existing Mallat rapid algorithm. On the basis of analyzing the thought of B-spline wavelet decomposition and reconstruction this paper emphatically studied the inherent relationship among the sys- tems of stretching drawing-back and translation of B-spline basic function under different scales, the solving process of reconstructed matrix was described by the use of clear geometric meanings. This algorithm is distinct in concept, simple in caleulation and stable on the result. Finally a living example was presented on decomposition and reconstruction of a complex curve by the use of this algorithm.