超小波发展综述

A survey of developments of super-wavelets

从问题发展的角度,论述了超小波在理论数学中的发展及其成果,简介了规范紧框架小波扩展为超小波的性质以及利用仿射结构构造超小波的方法,给出了一些公开问题,指出了新的研究方向.超小波是基于小波分析基础上的信号分析方法,关于规范紧框架小波扩展成超小波已经得到了一些重要结果,但是规范紧框架小波扩展为超小波的充分和必要条件还是一个公开问题,而且关于MRA超小波的一些重要方面也是公开的.

From the development of the problem, developments the super-wavelets in theory mathematics and their achievements are discussed. The characters of extending a normalized tight frame wavelet to a super-wavelet and the construction methods of super-wavelets by using affine structure are introduced. Lastly, a few open problems are listed and some new possible directions of research one pointed out. The super-wavelet is a signal analysis method based on wavelet analysis. There are some important results on extending a normalized tight frame wavelet to a super-wavelet, but there are some open problems on finding a sufficient and necessary condition for a normalized tight frame wavelet to be extended to a super-wavelet and the important aspects of the MRA super-wavelets also open.