紧支撑4-进双对称正交小波基

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。

Compactly Supported 4-bank Bisymmetric Orthonormal Wavelet Bases

This paper defines a new concept of bi-symmetry for multi-bank wavelets. By extending the theory of multi-resolution analysis to multi-bank wavelets,this paper also focuses on the study of 4-bank compactly supported bi-symmetric orthonormal wavelets. Investigates have shown that there is a class of 4-bank compactly supported 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 wavelets can process the boundary conveniently,and enjoy the highly efficient computations in application. This class of wavelets can provide lots of choices for application.