| 紧支撑正交的二维小波 |
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| 引用本文： | 何永滔.紧支撑正交的二维小波[J].纯粹数学与应用数学,2012(1):8-16. |
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| 作者姓名： | 何永滔 |
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| 作者单位： | 中山大学数学与计算科学学院 |
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| 基金项目： | 国家自然科学基金(11071261,10911120394) |
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| 摘 要： | 基于Householder矩阵扩充，构造了紧支撑正交的二维小波，所构造小波函数的支撑不超过尺度函数的支撑，并且给出了容易实施的显式构造算法．另外，还通过构造反例说明Riesz定理不适用于二元三角多项式．最后，构造了算例．
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| 关 键 词： | 多分辨分析 仿酉矩阵扩充 二维正交小波 多相位分解 Riesz定理 |
Compactly supported orthogonal bivariate wavelets |
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| He Yongtao.Compactly supported orthogonal bivariate wavelets[J].Pure and Applied Mathematics,2012(1):8-16. |
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| Authors: | He Yongtao |
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| Institution: | He Yongtao(School of Mathematics and Computational Science,Sun Yat-sen University,Guangzhou 510275,China) |
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| Abstract: | Based on the Householder matrix extension method,we construct compactly supported orthogonal bivariate wavelets.The supports of the constructed wavelets are not larger than that of scaling function,an explicit algorithm that can be easily applied is also presented.Furthermore,we prove that Riesz theorem can not be applied to bivariate trigonometrical polynomial.Finally,an example is given. |
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| Keywords: | multiresolution analysis paraunitary matrix extension bivariate orthogonal wavelets polyphase decomposition riesz theorem |
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