| 薛艳梅,毕宁.一类$L^2(\mathbb{R}^n)$的紧支撑不可分正交小波[J].数学研究及应用,2013,33(2):209~220 |
| 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 $L^2(\mathbb{R}^n)$ |
| 投稿时间：2011-11-10 修订日期：2012-02-20 |
| DOI：10.3770/j.issn:2095-2651.2013.02.008 |
| 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. |
| 基金项目:广东省计算科学重点实验室资助项目. |
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| 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. |
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