紧支撑4-进双对称正交小波基  

Compactly Supported 4-bank Bisymmetric Orthonormal Wavelet Bases

作　　者：王国秋[1] 郑果[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410083

出　　处：《世界科技研究与发展》2006年第2期61-65,47,共6页World Sci-Tech R&D

基　　金：国家自然科学基金资助;项目编号为No.10571049。

摘　　要：本文定义了一个双对称性新概念。通过将多分辨分析扩展到多进小波的办法,本文也构造了一个具有双对称性、紧支撑集和高阶消失矩的4-进正交小波类。研究表明该小波类可以由它的低通滤波器唯一确定,因而其余的自由度就可以施加到应用背景上,由此而得到的小波也有高效的计算实现。同时该小波具有很好的边界处理方案。该小波类为应用研究提供了大量的选择。This paper defines a new concept of bi-symmetry for multi-bank wavelets. By extending the theory of multiresolution analysis to multi-bank wavelets, this paper also focuses on the study of 4-bank compactly supported hi-symmetric orthonormal wavelets. Investigates have shown that there is a class of 4-bank compactly suplxrtted orthonormal wavelets with bi-symmetry, in which any wavelet system can be determined uniquely by its low-pass filter. Thus, the least restrictive conditions are needed for forming a wavelet so that the free degrees can be reserved for application requirement. Some concrete examples with high vanishing moments are also given. These wavdets can process the boundary conveniently,and enjoy the highly efficient computations in application. This class of wavdets can provide lots of choices for application.

关 键 词：4-进小波 正交小波 双对称性 图像编码 

分 类 号：TN911[电子电信—通信与信息系统]