基于二维康托尔二元群的小波变换  

The wavelet transform based on the two dimension Cantor binary group

作　　者：师东利 李万社[1] 

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《纺织高校基础科学学报》2017年第3期311-317,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11571213)

摘　　要：根据经典的康托尔集构造了二维康托尔集,将一维康托尔二元群上的小波变换推广到二维康托尔二元群上.利用一维多分辨分析的张量积构造出二维可分离多分辨分析,提出相应的尺度函数和小波函数,并给出基于该小波的分解与重构算法.According to the classic Cantor group,the two dimensional Cantor group was constructed,and the wavelet transformation was generalized from one-dimensional Cantor dyadic group to two-dimensional Cantor dyadic group.Using the tensor product of one dimensional multiresolution analysis,the two-dimensional separable multiresolution analysis was constructed.The scaling function and wavelet function were proposed,and the decomposition and reconstruction algorithm based on above MRA are given.

关 键 词：二维康托尔集 二维康托尔二元群 多分辨分析 分解与重构 

分 类 号：O174.2[理学—数学]