二维紧支撑正交多尺度函数的构造  

Construction of bivariate compactly supported orthogonal multiscaling functions

作　　者：谢长珍[1] 杨守志[1] 

机构地区：[1]汕头大学数学系,广东汕头515063

出　　处：《纺织高校基础科学学报》2006年第3期221-225,共5页Basic Sciences Journal of Textile Universities

基　　金：广东省自然科学基金资助项目(032038;04300917;05008289)

摘　　要：提出了由二维单正交的尺度函数构造二维紧支撑正交的多尺度函数的构造方法,并给出相应组合系数应满足的条件.研究表明,二维正交多尺度函数可由所给二维单正交的尺度函数的线性组合而成,这种由正交的单尺度函数构造出来的多尺度函数不是惟一的,但其平移伸缩构成的空间与相应单尺度函数的平移伸缩生成的子空间相同.A new approach of construction bivariate compactly supported orthogonal multi-scaling functions is presented by any given bivariate orthogonal uni-scaling function. The sufficient condition on combination coefficients is given. It is observed that the bivariate orthogonal multi-scaling function is a linear combination of given bivariate orthogonal uni-scaling function. In addition, the multi-scaling function constructed by using the method is not unique. The subspace generated by translates and dilations of every multiscaling function is the same as the subspace constructed by that of bivariate unl-scaling function.

关 键 词：二维正交的单尺度函数 二维正交的多尺度函数 滤波带 

分 类 号：O174.2[理学—数学]