| 一维连续小波变换 |
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| 引用本文： | 施云惠,阮秋琦. 一维连续小波变换[J]. 高等学校计算数学学报, 2007, 29(1): 1-8 |
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| 作者姓名： | 施云惠 阮秋琦 |
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| 作者单位： | 北京工业大学计算机学院多媒体与智能软件技术北京市重点实验室,北京,100022;北京交通大学信息科学研究所,北京,100044 |
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| 基金项目： | 国家自然科学基金(60572104,60533030,60375007)，北京市自然科学基金资助(40410031,4061001) |
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| 摘 要： | 1引言小波分析是近年来迅速发展起来的一门新兴学科,小波分析最显著的特征是频域和时域具有良好局部化特性,可以观察函数的任意细节,被誉为数学的显微镜．它不仅理论深刻,且理论与应用的发展交织在一起,它成功地应用于信噪分离、图像编码、图像的边缘检测、数据压缩、计算机视觉中的多分辨率分析等领域．
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| 关 键 词： | 连续小波变换 一维 多分辨率分析 小波分析 图像编码 局部化特性 计算机视觉 新兴学科 |
| 修稿时间： | 2003-07-16 |
CONTINUOUS WAVELET TRANSFORMS IN ONE DIMENSION |
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| Shi Yunhui,Ruan Qiuqi. CONTINUOUS WAVELET TRANSFORMS IN ONE DIMENSION[J]. Numerical Mathematics A Journal of Chinese Universities, 2007, 29(1): 1-8 |
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| Authors: | Shi Yunhui Ruan Qiuqi |
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| Affiliation: | Beijing Municipal Multimedia and Intelligent Software Key Laboratory, College of Computer Science, Beijing University of Technology Beijing 100022;Institute of Information Science, Beijing Jiaotong University, Beijing 100044 |
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| Abstract: | In view of the inverse transform of the classical continuous wavelet transform,the variables of integral a and b are independent.As the discretizations a_k,b_l of a and b are dependent,for example b_l=a_klbo where b_O is a constant,the corresponding numerical integral has high resolution.In the inverse transform a appears in the denominator of integrand.While|a|becomes smaller,the error of the numerical integral will grow bigger.So we construct a new type of continuous wavelet transform and its inverse transform.However we discretize a and b,any numerical integral has a high resolution,and a does not appear in the denominator of the integrand.The numerical examples show that the continuous wavelet trans- form constructed in this paper has great advantage compared with the classical continuous wavelet transform.Finally,the relative numerical method is proposed, The numerical examples demonstrate that the continuous wavelet transform con- structed in this paper is effective. |
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| Keywords: | fourier transform continuous wavelet transform wavelet frame |
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