We construct classes of nonstationary wavelets generated by what we call spherical basis functions (SBFs), which comprise a subclass of Schoen-berg's positive deenite functions on the m-sphere. The wavelets are intrinsically deened on the m-sphere, and are independent of the choice of coordinate system. In addition, they may be orthogonalized easily, if desired. We will discuss decomposition, r...

The numerical solutions to the nonlinear integral equations of Hammerstein-type y(t) =f(t) + 11 k(t,s)g(s,y(s))ds, t E [0,1] with using Daubechies wavelets are investigated. A general kernel scheme basing on Daubechies wavelets combined with a collocation method is presented. The approach of creating Daubechies interval wavelets and their main properties are briefly mentioned. Also we present a...

In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C1 and supported on [−1, 1]. Moreover, one wavelet is symmetric, and the other is antisymmetric. These spline wavelets are then adapted to the interval [0, 1]. The construction of boundary wavelets is remarkably simple. Furthermore, global stability of the wavelet basis is established. ...

The theory of RS2] is applied to yield compactly supported tight aane frames (wavelets) in L 2 (IR d) from box splines. The wavelets obtained are smooth piecewise-polynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of \mother wavelets", however, increases with the increase of the required smoothness. Two bivariate const...

This paper is on the angle-frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration, scaling function...

In this paper we investigate spline wavelets on general triangulations. In particular, we are interested in C1 wavelets generated from piecewise quadratic polynomials. By using the Powell-Sabin elements, we set up a nested family of spaces of C1 quadratic splines, which are suitable for multiresolution analysis of Besov spaces. Consequently, we construct C1 wavelet bases on general triangulatio...

This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is aimed at preserving isotropy, and a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. Resulting three oriented high-pass filters are symmetrically...

In this paper we investigate spline wavelets on general triangulations. In particular, we are interested in C1 wavelets generated from piecewise quadratic polynomials. By using the Powell-Sabin elements, we set up a nested family of spaces of C1 quadratic splines, which are suitable for multiresolution analysis of Besov spaces. Consequently, we construct C1 wavelet bases on general triangulatio...

This paper aims to obtain approximate solutions of the one-dimensional nonlinear Klein-Gordon equation by employing Cubic B-spline wavelets. Our scheme uses the Galerkin method and approximates the solution in the terms of cubic B-spline scaling and wavelet functions. These wavelets are applied as testing and weighting functions. Because of some properties of these wavelets such as having compa...

This paper presents an eecient algorithm to generate realistic images using spline wavelets. Our algorithm departs from the use of non-overlapping wavelets by providing a continuous solution at no extra cost. This in turn eliminates need for inaccurate Gouraud shading or expensive nal gather step. Advantage of spline wavelets come from the fact that scaling functions are n th order B-splines th...