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...

Complex approximately analytic wavelets provide a local multiscale description of images with good directional selectivity and invariance to shifts and in-plane rotations. Similar to Gabor wavelets, they are insensitive to illumination variations and facial expression changes. The complex wavelet transform is, however, less redundant and computationally efficient. In this paper, we first constr...

In this paper an attempt has been made to derive the lifting scheme for a set of new bi-orthogonal wavelets and apply on image compression. Four new bi-orthogonal wavelets are designed by taking different basis functions which are selected so as to capture the sharp edges which are common in images. For these classical wavelets, lifting versions are calculated and presented in this paper. The l...

For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including eecient numerical estimates if the number L of decomposition levels is small, as well as growth estima...

This chapter takes up the design of discrete wavelet transforms based on oversampled filter banks. In this case the wavelets form an overcomplete basis, or frame. In particular, we consider the design of systems that are analogous to Daubechies’ orthonormal wavelets — that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case....

Drought forecasting is essential for risk management and preparedness of drought mitigation measures. The present study aims to evaluate the effectiveness proposed hybrid technique regional forecasting. Multiple Linear Regression (MLR), Artificial Neural Network (ANN), two wavelet techniques, namely, Discrete Wavelet Transform (DWT) Packet (WPT), were evaluated in up a lead time six months. Sta...