摘要
基于Householder矩阵扩充,构造了紧支撑正交的二维小波,所构造小波函数的支撑不超过尺度函数的支撑,并且给出了容易实施的显式构造算法.另外,还通过构造反例说明Riesz定理不适用于二元三角多项式.最后,构造了算例.
Based on the Householder matrix extension method, we construct compactly supported orthogonal bivariate wavelets. The supports of the constructed wavelets are not larger than that of scaling function, an explicit algorithm that can be easily applied is also presented. Furthermore, we prove that Riesz theorem can not be applied to bivariate trigonometrical polynomial. Finally, an example is given.
出处
《纯粹数学与应用数学》
CSCD
2012年第1期8-16,共9页
Pure and Applied Mathematics
基金
国家自然科学基金(11071261
10911120394)
关键词
多分辨分析
仿酉矩阵扩充
二维正交小波
多相位分解
RIESZ定理
multiresolution analysis, paraunitary matrix extension, bivariate orthogonal wavelets, polyphase decomposition, riesz theorem
