The Constructing Theory Of Armlet And Two-direction Wavelet

In chapter 1 and 2, we introduce the basic theories of MRA, wavelet andmultiwavelet. Analysis-ready multiwavelets (Armlets) is introduced. Based onthe existing orthogonal multiwavelets, a new constructing arithmetic of Armletsis given.In chapter 3, we introduce the concept of two-direction refinable functionsand two-direction wavelets with dilation factor m. We investigate the followingtwo-direction refinement equation:φ(x)=sum from n=k p_k~+φ(mx-k)+sum from n=k p_k~-φ(k-mx), where m≥2 is an integer. Here, we call the two sequences {p_k~+}_k and {p_k~-}_kpositive mask and negative mask respectively. Based on the positive mask andnegative mask, the conditions that the above equation has compactly distribu-tional solutions are established. The conditions that the above equation hasL~2-stable solutions are also presented. The support ofφ(x) is discussed amply.A algorithm for constructing orthogonal two-direction refinable functions andtheir orthogonal wavelets is presented. Based on the orthogonal two-directionrefinable functions and two-direction wavelets, orthogonal and symmetric mul-tiscaling functions and their multiwavelets can be constructed easily.