高维小波框架包子空间对空间L2(Rn)的分解

doi:10.6040/j.issn.1671-9352.0.2018.058

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (8): 34-42.doi: 10.6040/j.issn.1671-9352.0.2018.058

高维小波框架包子空间对空间L²(Rⁿ)的分解

盖晓华¹,郭学军^2*,冯金顺²,陈清江³,程正兴⁴

1. 南阳理工学院电子与电气工程学院, 河南南阳 473004;2. 南阳理工学院数学与统计学院, 河南南阳 473004;3. 西安建筑科技大学理学院, 陕西西安 710055;4.西安交通大学数学与统计学院, 陕西西安 710049

收稿日期:2018-01-31 出版日期:2018-08-20 发布日期:2018-07-11
作者简介:盖晓华(1967— ),女,教授,硕士,研究方向为智能控制、小波分析. E-mail:gaixiaohua@163.com*通信作者简介:郭学军(1966— ),男,教授,研究方向为系统建模、小波分析. E-mail:gxuejun66@163.com
基金资助:
国家自然科学基金资助项目(61504072);河南省自然科学基金资助项目(102300410022)

Decomposition for L2(Rⁿ)by subspaces composed of high-dimensional tight framelet packets

GAI Xiao-hua¹, GUO Xue-jun^2*, FENG Jin-shun², CHEN Qing-jiang³, CHENG Zheng-xing⁴

1. School of Electronic and Electrical Engineering, Nanyang Institute of Technology, Nanyang 473004, Henan, China;
2. School of Mathematics and Statistics, Nanyang Institute of Technology, Nanyang 473004, Henan, China;
3. School of Science, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China;
4. School of Mathematics and Statistics, Xian Jiaotong University, Xian 710049, Shaanxi, China

Received:2018-01-31 Online:2018-08-20 Published:2018-07-11

摘要/Abstract

摘要： 研究小波框架包子空间对空间L²(Rⁿ)的分解。运用时频分析方法与逼近论思想,刻画了数量矩阵伸缩的高维小波框架包的特征,构造了若干高维小波框架包子空间,进而,由小波框架包子空间得到了L²(Rⁿ)的直交分解式。给出高维小波框架包函数的频域表达式,类似于正交基,提出高维紧小波框架包构成空间L²(Rⁿ)的巴塞尔框架的充分条件,扩展了小波框架应用范围。

关键词: 面具函数, 扩张原理, 生成元, 小波框架, 小波框架包

Abstract: The decomposition for space L²(Rⁿ)by subspaces composed of framelet packets are investigated. The characteristics of the high-dimensional wavelet frame packets with a quantity dilation matrix are described by using time-frequency analysis method and functional analysis method. The subspaces from the high-dimensional framelet packets are constructed. Moreover the direct decomposition for space L²(Rⁿ)is obtained from these subspaces composed of framelet packets. The frequency-field formulas for the high-dimensional framelet packets are presented. A sufficient condition is suggested that a Parseval frame constituted from the high-dimensional tight framelet packets of space L²(Rⁿ). These enrich the wavelet frame theory, so that they can be applied to a wider range.

Key words: wavelet frames, framelet packets, expansion principle, mask functions, generators

中图分类号:

O174.2

盖晓华,郭学军,冯金顺,陈清江,程正兴. 高维小波框架包子空间对空间L²(Rⁿ)的分解[J]. 山东大学学报（理学版）, 2018, 53(8): 34-42.

GAI Xiao-hua, GUO Xue-jun, FENG Jin-shun, CHEN Qing-jiang, CHENG Zheng-xing. Decomposition for L2(Rⁿ)by subspaces composed of high-dimensional tight framelet packets[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 34-42.

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高维小波框架包子空间对空间L²(Rⁿ)的分解

Decomposition for L2(Rⁿ)by subspaces composed of high-dimensional tight framelet packets

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