| N维2带小波紧框架的构造 |
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| 引用本文： | 何永滔. N维2带小波紧框架的构造[J]. 系统科学与数学, 2010, 10(10): 1368-1378 |
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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,广州,510275 |
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| 摘 要： | 给出了$m$个函数生成$N$维2带小波紧框架的充分条件和$N$维2带小波紧框架的显式构造算法, 讨论了小波紧框架的分解算法与重构算法. 提出的构造方法很有普遍性, 容易推广到$N(Ngeq2)$维$M(Mgeq 2)$带小波紧框架的情形,也可以得到类似的小波紧框架的分解算法与重构算法.
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| 关 键 词： | 小波紧框架 尺度函数 框架多分辨分析. |
| 收稿时间： | 2009-11-20 |
CONSTRUCTION OF N-DIMENSIONAL TWO-BAND TIGHT WAVELET FRAMES |
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| HE Yongtao. CONSTRUCTION OF N-DIMENSIONAL TWO-BAND TIGHT WAVELET FRAMES[J]. Journal of Systems Science and Mathematical Sciences, 2010, 10(10): 1368-1378 |
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| Authors: | HE Yongtao |
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| Affiliation: | College of Mathematics and Computation Science, Sun Yat-Sen University, Guangzhou 510275 |
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| Abstract: | In this paper, sufficient condition for $N$-dimensional two-band tight wavelet frames and explicit algorithm for the construction of tight wavelet frames arepresented. The decomposition and reconstruction formulas of $N$-dimensional two-band tight wavelet frames are also provided. The methods presented here have generality, the $N$-dimensional $M$-band tight wavelet frames can be constructed similarly, and the similar decomposition and reconstruction formulas of tight wavelet frames can be obtained. |
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| Keywords: | Tight wavelet frames scaling function frame multiresolution analysis. |
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