Construction of Biorthogonal Wavelets by CBC
نویسنده
چکیده
In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental reenable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For example, we shall see that any orthogonal scaling function, which is supported on 0; 2r ? 1] s for some positive integer r and has accuracy order r, has Lp (1 p 1) smoothness not exceeding that of the univari-ate Daubechies orthogonal scaling function which is supported on 0; 2r ? 1]. Similar results hold true for fundamental reenable functions and biorthogonal wavelets. Then, we shall discuss the relation between symmetry and the smoothness of a reenable function. Next, we discuss the coset by coset (CBC) algorithm reported in Han 29] to construct biorthogonal wavelets with arbitrary order of vanishing moments. We shall generalize this CBC algorithm to construct bivariate biorthogonal wavelets. For any positive integer k and a bi-variate primal mask a such that a is symmetric about the origin, such CBC algorithm provides us a dual mask of a such that the dual mask satisses the sum rules of order 2k and is also symmetric about the origin. The resulting dual masks have certain optimal properties with respect to their support. Finally, examples of bivariate biorthogonal wavelets constructed by the CBC algorithm are provided to illustrate the general theory. Advantages of the CBC algorithm in this paper over other methods on constructing biorthogonal wavelets are also discussed.
منابع مشابه
Construction of Multivariate Biorthogonal Wavelets by CBC Algorithm
In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental refinable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For exampl...
متن کاملConstruction of Biorthogonal Wavelets by CBC Algorithm
In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental reenable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For example...
متن کاملAnalysis and Construction of Optimal Multivariate Biorthogonal Wavelets with Compact Support
In applications, it is well known that high smoothness, small support and high vanishing moments are the three most important properties of a biorthogonal wavelet. In this paper, we shall investigate the mutual relations among these three properties. A characterization of Lp (1 ≤ p ≤ ∞) smoothness of multivariate refinable functions is presented. It is well known that there is a close relation ...
متن کاملProceedings of the International Conference on Wavelet Analysis and Applications
In this paper, we shall discuss how to construct multidimensional biorthogonal wavelets by employing a coset by coset (CBC) algorithm. We shall construct biorthogonal wavelets on the hexagonal lattice by CBC algorithm. In particular, we shall propose a CBC algorithm to construct inter-polatory biorthogonal wavelets which are derived from pairs of fundamental reenable functions. More precisely, ...
متن کامل