The biorthogonal wavelets introduced by Cohen, Daubechies, and Feauveau contain in particular compactly supported biorthogonal spline wavelets with compactly supported duals. We present a new approach for the construction of compactly supported spline wavelets, which is entirely based on properties of splines in the time domain. We are able to characterize a large class of such wavelets which c...

We describe a method to construct a hierarchical representation of a given implicitly defined algebraic spline curve with the help of weighted spline wavelets. These wavelets are adapted to the region of interest, in our case to the region along the curve, by means of a weighted inner product. The application of two different types of weighted spline wavelets is considered and compared with sta...

in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...

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, ...

Battle-Lemari e's wavelet has a nice generalization in the bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the lters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass lter when the degree of the bivariate box spline functions increases to 1. The passing and stopping bands of the ideal lter are dependent ...

We give a formula for the duals of the masks associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.