| Gauss小波变换像空间的描述 |
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| 引用本文： | 邓彩霞,曲玉玲,侯杰. Gauss小波变换像空间的描述[J]. 数学学报, 2008, 51(2): 225-234. DOI: CNKI:SUN:SXXB.0.2008-02-004 |
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| 作者姓名： | 邓彩霞 曲玉玲 侯杰 |
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| 作者单位： | [1]哈尔滨理工大学应用科学学院,哈尔滨150080 [2]南京航空航天大学民族学院,南京210016 [3]黑龙江八一农垦大学文理学院,大庆163319 |
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| 基金项目： | 国家自然科学基金资助项目（10571037）;黑龙江省教育厅高校骨干教师创新项目（1054G010） 致谢 作者对审稿人表示衷心感谢. |
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| 摘 要： | 在连续小波变换像空间是再生核Hilbert空间的基础上,针对经常用于边界检测并且使用效果非常好的Gauss小波,给出了其小波变换像空间的再生核具体表达式.并且当固定尺度因子和固定平移因子时,利用再生核空间理论,对Gauss小波变换像空间做了具体描述,分别给出了Gauss小波变换像空间中的等距恒等式和反演公式,这为进一步研究一般的小波变换像空间提供了理论基础.
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| 关 键 词： | 小波变换 再生核 Gauss小波 |
| 文章编号： | 0583-1431（2008）02-0225-10 |
| 收稿时间： | 2006-01-17 |
| 修稿时间： | 2007-07-06 |
Characterization of Image Space of Gauss Wavelet Transform |
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| Cai Xia DENG Yu Ling QU Jie HOU. Characterization of Image Space of Gauss Wavelet Transform[J]. Acta Mathematica Sinica, 2008, 51(2): 225-234. DOI: CNKI:SUN:SXXB.0.2008-02-004 |
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| Authors: | Cai Xia DENG Yu Ling QU Jie HOU |
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| Affiliation: | Cai Xia DENG Applied Science College, Harbin University of Science and Technology, Harbin 150080, P. R. China Yu Ling QU College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China College of Arts and Science, Heilongjiang August First Land Reclamation and Cultivation University, Daqing 163319, P. R. China |
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| Abstract: | For the Gauss wavelet which is often used in edge detection and is of a good performance, the expression of the reproducing kernel function of image space of Gauss wavelet transform is shown on the bases of the image space of the continuous wavelet transform being a reproducing kernel Hilbert space. And when scale factor and translation factor are fixed, a concrete characterization of image space of Gauss wavelet transform is given by the theory of reproducing kernel function, and the isometric identities and the inversion formulas are obtained respectively, which provides a theoretical basis for us to study the theory of image space of the general wavelet transform. |
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| Keywords: | wavelet transform reproducing kernel Gauss wavelet |
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