| 基于L~1度量分析的图象分解与重构算法 |
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| 引用本文： | 李峰,杨力华,黄达人.基于L~1度量分析的图象分解与重构算法[J].计算数学,2003,25(4):493-504. |
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| 作者姓名： | 李峰 杨力华 黄达人 |
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| 作者单位： | 1. 中山大学科学计算与计算机应用系,广州,510275;长沙理工大学计算机与通信工程学院,长沙,410076
2. 中山大学科学计算与计算机应用系,广州,510275 |
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| 基金项目： | 广东省自然科学基金重点项目(036608)、广州市科技计划项目及国家自然科学基金(60172067)资助. |
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| 摘 要： | Mallat‘s decompositon and reconstruction algorithms are very important in the the field of wavelet theory and its applications to signal processing.Wavelet Anal-ysis,which is based on L^2(R) space,can eliminate redundancy of signals with the help of orthogonality and characterize the processing precision with the meansquare error.In the recent years,it is understood that the mean square measuredoes not match human visual sensitivity well.From the point of view,R.DeVore studied L^1 measure instead.Similarly,considering the principles of image com-pression,Yang introduced and dealt with orthogonality in L^1 space based on thebest approximation theory,and consequently established the corresponding decom-position and reconstruction algorithms for signals.In this paper,error analyses for the algorithms above are taken and the selection of the best parameters in the algorithms are discussed in detail.Finally,the algorithms are compared with the classical Haar and Daubechies‘‘s orthogonal wavelets based on the singal-to-noiseratio data computed.
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| 关 键 词： | 小波变换 Mallat算法 均方逼近度 内积空间 均方误差 图象处理 L^1度量分析 |
| 修稿时间： | 2002年6月28日 |
DECOMPOSITION AND RECONSTRUCTION ALGORITHMS BASED ON L~1 MEASURE ANALYSIS |
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| Li Feng.DECOMPOSITION AND RECONSTRUCTION ALGORITHMS BASED ON L~1 MEASURE ANALYSIS[J].Mathematica Numerica Sinica,2003,25(4):493-504. |
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| Authors: | Li Feng |
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| Institution: | Li Feng Department of Scientific Computing and Computer Application Sun Yatsen University,
Guangzhou, 510275;
School of Computer and Communication Technology, Changsha University of Science and
Technology, Changsha, 410076
Yang Lihua Huang Daren
Department of Scientific Computing and Computer Application Sun Yatsen University,
Guangzhou, 510275 |
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| Abstract: | Mallat's decompositon and reconstruction algorithms are very important in the the field of wavelet theory and its applications to signal processing. Wavelet Analysis, which is based on L2(R) space, can eliminate redundancy of signals with the help of orthogonality and characterize the processing precision with the mean square error. In the recent years, it is understood that the mean square measure does not match human visual sensitivity well. From the point of view, R. DeVore studied L1 measure instead. Similarly, considering the principles of image compression, Yang introduced and dealt with orthogonality in L1 space based on the best approximation theory, and consequently established the corresponding decomposition and reconstruction algorithms for signals. In this paper, error analyses for the algorithms above are taken and the selection of the best parameters in the algorithms are discussed in detail. Finally, the algorithms are compared with the classical Haar and Daubechies's orthogonal wavelets based on the singal-to-noise ratio data computed. |
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| Keywords: | wavelet Mallat's algorithm approximation degree |
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