一类$L^2(\mathbb{R}^n)$的紧支撑不可分正交小波

A Class of Compactly Supported Nonseparable Orthogonal Wavelets of $L^2(\mathbb{R}^n)$

中文关键词:  不可分  多变量  正交  紧支撑  稳定性.

英文关键词:nonseparable  multivariate  orthogonal  compactly supported  stability.

中文摘要:

      本篇文章给出一类$L^{2}(\mathbb{R}^{n})$, $n\geq2$的紧支撑不可分正交小波基的具体构造算法,其中正交小波的伸缩矩阵为$\alpha I_{n}~(\alpha\geq2,\ \alpha \in \mathbb{Z})$, $I_{n}$是$n$阶单位矩阵.最后给出两个不可分正交小波基的构造算例.

英文摘要:

      In this paper, we present a concrete method for constructing a class of compactly supported nonseparable orthogonal wavelet bases of $L^{2}(\mathbb{R}^{n}),\ n \geq2$. The orthogonal wavelets are associated with dilation matrix $\alpha I_{n}\ (\alpha\geq2,\ \alpha \in \mathbb{Z})$, where $I_{n}$ is the identity matrix of order $n$. In the end, two examples are given to illustrate how to use our method to construct nonseparable orthogonal wavelet bases.