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...

We introduce a new approach in order to construct a wavelets with arbitrary support on the interval. This result allows us to adapt on the interval some important classes of wavelets (coiflets, symlets, Lemarié's wavelets). In addition, we show how to obtain multiresolution analysis on the interval with better approximation rate in some neighborhood of the interval.

We improve Wang's characterization for a pair of biorthogonal wavelets to be associated with biorthogonal multiresolution analyses (MRA's). We show that one of the two conditions in his characterization is redundant, and, along the way, show that for a pair of biorthogonal wavelets to be associated with biorthogonal MRA's it is necessary and suÆcient that one of the wavelets is associated with ...

Abstract. We propose the application of hyperbolic interpolatory wavelets for large-scale -dimensional data fitting. In particular, we show how wavelets can be used as a highly efficient tool for multidimensional smoothing. The grid underlying these wavelets is a sparse grid. The hyperbolic interpolatory wavelet space of level uses basis functions and it is shown that under sufficient smoothnes...

Time series analysis is used extensively in neuroscience in order to study the interdependence between two simultaneously recorded signals (Pereda et al., 2005). Neurophysiological time series are inherently non-stationary, and the detection of changes in covariance structure is important as they reflect changes in the functional connectivity of the system. This, therefore, allows us to make in...