| 框架的冗余性及其对小波重构的影响 |
| |
| 引用本文： | 郅伟萍,曹怀信.框架的冗余性及其对小波重构的影响[J].宝鸡文理学院学报(自然科学版),2007,27(1):1-4. |
| |
| 作者姓名： | 郅伟萍 曹怀信 |
| |
| 作者单位： | 陕西师范大学,数学与信息科学学院,陕西,西安,710062;陕西师范大学,数学与信息科学学院,陕西,西安,710062 |
| |
| 基金项目： | Partial support was provided by the National Natural Science Foundation Grants of China （No. 10561113）. |
| |
| 摘 要： | 目的给出框架冗余性的一个刻画。方法定义了冗余框架。如果一个框架的指标集存在一个真子集使得也是一个框架,那么就说这个框架是冗余的,否则它就是非冗余的。结果经过研究得出了框架冗余的充分必要条件。特别地,一个框架是非冗余的当且仅当它是一个Riesz基。结论这些结果表明用冗余框架进行小波重构要比用正规正交基进行小波重构的误差小。
|
| 关 键 词： | 冗余性 框架 小波重构 |
| 文章编号： | 1007-1261（2007）01-0001-04 |
| 收稿时间： | 2006-09-26 |
| 修稿时间： | 2006-12-14 |
Redundancity of frames and its effects on the wavelet reconstruction |
| |
| ZHI Wei-ping,CAO Huai-xin.Redundancity of frames and its effects on the wavelet reconstruction[J].Journal of Baoji College of Arts and Science(Natural Science Edition),2007,27(1):1-4. |
| |
| Authors: | ZHI Wei-ping CAO Huai-xin |
| |
| Abstract: | Ai m Acharacterizationfor the redundancity of a frameis established.Methods A new definition on redundancity of a frame is presented.Aframe of Hilbert space is known as redundant if there exists a proper subset of the index set such that is also a frame.Otherwise,the frame is known as nonredundant.Results Necessary and sufficient conditions for a frame to be redundant are given.Especially,it is provedthat a frameis nonredundant if and onlyif it is a Riesz basis.Conclusion The results showthat the error in wavelet reconstruction with redundant frames is less than that with or-thonormal basis. |
| |
| Keywords: | redundancity frame wavelet reconstruction |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
