Characterization of Biorthogonal Cardinal Spline Wavelet Bases
نویسنده
چکیده
In both applications and wavelet theory, the spline wavelets are especially interesting, in part because of their simple structure. In a previous paper we proved that the function m;l is an m th order spline wavelet having an l th order spline dual wavelet. This enabled us to derive biorthogonal spline wavelet bases. In this paper we rst study the general structure of cardinal spline wavelets, and then give the characterization of biorthogonal cardinal spline wavelets bases. We also prove that the function m;l is an minimally supported m th order cardinal spline wavelet having an l th order cardinal spline dual wavelet. various properties of the wavelet m;l are given.
منابع مشابه
Biorthogonal Spline Wavelets on the Interval
We investigate biorthogonal spline wavelets on the interval. We give sufficient and necessary conditions for the reconstruction and decomposition matrices to be sparse. Furthermore, we give numerical estimates for the Riesz stability of such bases. §
متن کاملBiorthogonal Box Spline Wavelet
Some speciic box splines are reenable functions with respect to nn expanding integer scaling matrices M satisfying M n = 2I: Therefore they can be used to deene a multiresolution analysis and a wavelet basis associated with these scaling matrices. In this paper, we construct biorthogonal wavelet bases for this special subclass of box splines. These speciic bases can also be used to derive wavel...
متن کاملBiorthogonal wavelet bases for the boundary element method
As shown by Dahmen, Harbrecht and Schneider [7, 23, 32], the fully discrete wavelet Galerkin scheme for boundary integral equations scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. The supposition is a wavelet basis with a sufficiently large number of vanishing moments. In this paper we present several constructions of appropriate ...
متن کامل(Microsoft Word - spie2003.doc)
We show that a multi-dimensional scaling function of order γ (possibly fractional) can always be represented as the convolution of a polyharmonic B-spline of order γ and a distribution with a bounded Fourier transform which has neither order nor smoothness. The presence of the B-spline convolution factor explains all key wavelet properties: order of approximation, reproduction of polynomials, v...
متن کاملStable Lifting Construction of Non-Uniform Biorthogonal Spline Wavelets with Compact Support
In this paper we use the lifting scheme to construct biorthogonal spline wavelet bases on regularly refined non-uniform grids. The wavelets have at least one vanishing moment and on each resolution level they form an L2 Riesz basis. Furthermore we are interested in determining the exact range of Sobolev exponents for which the complete multilevel system forms a Riesz basis. Hereto we need to ex...
متن کامل