On The Construction Of Multiwavelet And Two-direction Multiwavelet

The multiwavelet is the single wavelet promotion.It also has a compactlysupported,orthogonal,symmetry,high vanishing moments.Thus causing thewidespread interest.As we known,two-scale refinable equation plays a basic role in construction andapplications of scalar wavelets.The scaling vectors functions with nonnegative masksplay a very important role in engineering,and there are many researchers into suchvector functions.Two-direction refinement equation is researched by Yang Shou Zhi Professor atscience in china and a series of SCI magazine put forword the concept of thetwo-direction wavelet in2007,that is:φ(x)=∑P_k~+φ(mx-k)+∑P_k~-φ(k-mx)And an algorithm for constructing two-direction refinable functions andtwo-direction wavelets with high approximation order and regularity.Two-directionwavelets is the traditional form of wavelet. Introduction of two-direction waveletstake a step for development of wavelets theory. Professor Yang Shouzhi discusstwo-direction wavelets, Soon-Geol Kwon discuss the two-direction multiwavelettheory at the journal SCI of Applied Mathematics and computation in2012, but theconstruction of two-direction multiwavelet still have a lot of work to be done.In this paper, we are at the basis of depth understanding of the research status ofwavelet theory at home and abroad,focus on the depth constrection theory oftwo-direction multiwavelet theory and construction algorithm. Specifically:The three chapter, research in the construction of a class of two-direction orthogonalconjugate filters,given constructing algorithms and numerical examplesThe four chapter, research in the construction a class of compactly supportedsymmetric-antisymmetric two-direction multiwavelet. given constructing algorithmsand numerical examplesThe five chapter, discussed the construction of a scale compactly supportedtwo-direction orthogonal multiwavelet and its related properties. given constructingalgorithms and numerical examplesThe six chapter, discussed the construction of r multiplicity two-dimensionalorthogonal multiwavelet and an example is given.Research results enrich the construct theory of Multiwavelet and two-directinmultiwavelets...