New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet’s solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is related to the solution of a Mathieu equation of odd characteristic exponent. The number of notches of these analysing filters can be easily designed. Wavelet...

An adaptive numerical method for solving partial differential equations is developed. The method is based on the whole new class of second-generation wavelets. Wavelet decomposition is used for grid adaptation and interpolation, while a new O(N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The treatment o...

In this paper we study some problems related with the theory of multidimensional p-adic wavelets in connection with the theory of multidimensional p-adic pseudo-differential operators (in the p-adic Lizorkin space). We introduce a new class of n-dimensional p-adic compactly supported wavelets. In one-dimensional case this class includes the Kozyrev p-adic wavelets. These wavelets (and their Fou...

The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number of Minimally Supported Frequency (MSF) wavelets, so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L2-norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Althoug...

Discrete wavelet transform is an effective tool to generate scalable stream, but it cannot efficiently represent edges which are not aligned in horizontal or vertical directions, while natural images often contain rich edges and textures of this kind. Hence, recently, intensive research has been focused particularly on the directional wavelets which can effectively represent directional attribu...

We investigate a very general subset of two-dimensional, orthogonal, compactly supported wavelets. This subset includes all the wavelets with a corresponding wavelet (polyphase) matrix that can be factored as a product of factors of degree-1 in one variable. In this paper we consider in particular wavelets with vanishing moments. The number of vanishing moments that can be achieved increases wi...

Effective wavelets to solve electromagnetic integral equations are proposed. It is based on the same construction procedure as Daubechies wavelets but with mix-phase to obtain maximum sparsity of moment matrix. These new wavelets are proved to have excellent performance in non-zero elements reduction in comparison with minimum-phase wavelet transform (WT). If further sparsity is concerned, wave...

Two-dimensional compactly supported, orthogonal wavelets and lter-banks having linear phase are presented. Two cases are discussed, wavelets with twofold symmetry (centrosymmetric), and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of factorable wavelets, imposes a...

2 SUMMARY In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advant...