On The Construction Of Two-direction Wavelets And Two-direction Multi-Wavelets

Wavelets analysis has developed on modern harmonic analysis, it has been the hot s pot of theory research since it was presented.Construction of wavelets analysis is the core issue of wavelets analysis. As we known, two-scale refinable equation plays a basic role in construction and applications of scalar wavelets.The scaling vectors functions with nonnegative masks play a very important role in engineering, and there are many researchers into such vector functions.Two-direction refinement equation is presented by Yang Shouzhi professor, that is: and an algorithm for constructing two-direction refinable functions and two-direction wavelets with high approximation order and regularity.Two-direction wavelets is the traditional form of wavelets. Introduction of two-direction wavelets take a step for development of wavelets theory,and property theory and construction algorithm research are become a hot issue. Yang Shouzhi professor only discuss two-direction wavelets, but he does not discuss theory of two-direction multi-wavelets. So theory of two-direction multi-wavelets are given as following. We understand intensively based on of home and abroad wavelets theory, discuss theory of two-direction multi-wavelet -s;Two-direction refinement functions with approximation order and symmetry theory; two-direction multi-wavelets decomposition and reconstructing algorithm; constructio -n of two-direction multi-wavelets packets algorithm. Based on the algorithm theory, several examples are given and we draw the picture of them.Specifically:The three chapter, based on one-direction wavelets, we discuss theory of two-directio -n multi-wavelets;The four chapter,we research two-direction multi-wavelets decomposition and reconst ucting algorithm, property of biorthogonal two-direction multi-wavelets packets are presented.The five chapter,with high approximation order and symmetry properties theory are discussed and two examples are given.Finally, based on the algorithm theory, three examples are given and we draw the picture of them.