【摘要】 引入了对应于高维多重尺度函数的多小波包,建立了具有矩阵伸缩的多小波包的理论框架,所产生的L2(Rn)的基称为多小波包基.给出具有任意矩阵伸缩的高维不可分正交多小波包的构造方法,进一步地表明如何从多小波中抽取L2(Rn)各种正交基,尤其是由于所构造的多小波分解可从不同的滤波器中的抽取,因而使得多小波基的选取更具灵活性.更多还原

【Abstract】 Multivariate multiwavelet packet, which allows the use of multiple scaling functions in higher dimensions, is introduced and the theory framework of multiwavelet packets is developed. The resulting basis of L2(Rn) is called the multiwavelet packet basis. A procedure for the construction of nonseparable orthogonal multiwavelet packets associated with arbitrary dilation matrix is presented. Furthermore, it is shown how to construct various orthogonal bases of L2(Rn) from the multiwavelet packets, and this makes it more flexible to choose multiwavelet basis because the multiwavelet packets decomposition constucted by the paper can be extracted out from all sorts of filters.更多还原