The Bidirectional Wavelet And Parseval-equation Number Of Issues Discussed

Wavelet analysis is a subject of applied mathematics.It's used widely and plays a very important role in theoretical and applied science,especially information science. And it also universally helps to non-linear science,intelligent computing,earthquake and earth of structure,tide. It is the key of wavelet analysis to do theoretical study that wavelet analysis is suitable for practical application and efficient promotion through new wavelets we find or improve the method of computation.In the paper,some special wavelets'Parseval-equations and new ways to con-struct wavelets will be found through Parseval-equations'generalization and two-direction old ways of wavelets'construction so that we can have the theoretical basis of the them.There are mainly two parts in the content of paper,the first part is about an important result in wavelet analysis,i.e.Parseval equation in 2-D dyadic wavelet;the second is about the decomposition and reconstruction algorithm of bi-variate two-direction biorthogonal multiwavelets.There are three parts in the paper: Chapter 1, an introduction to the develepment of two-direction wavelet analysis and two-refine function of theoory; Chapter 2,an introduction to 2-D dyadic wavelet's Parseval equations;Chapter 3,how to construct bivariate two-direction biorthogonal multiwavelets through the results of other people.Finally,the main concepts and some problems existed in the paper,plus the present situation of two-direction wavelet analysis and two-refine function, will be introduced.