Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases ooer a number of potential advantageous properties. For example, it has been recently suggested 1], 2] that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property then it must exhibit linear phase as well. ...

Previous analysis of high frequency nancial time series data has found volatility to follow a long-memory process and to display an intradaily U-shape pattern. These ndings implicitly assume that a stable environment exists in the nancial world. To better capture the nonstationary behavior associated with market collapses, political upheavals and news annoucements, we propose a nonstationary cl...

Shift-orthogonal wavelets are a new type of multiresolution wavelet bases that are orthogonal with respect to translation (or shifts) within one level but not with respect to dilations across scales. In this paper, we characterize these wavelets and investigate their main properties by considering two general construction methods. In the first approach, we start by specifying the analysis and s...

Wavelets have recently been a subject of great interest in geophysics, mathematics and signal processing. The discrete wavelet transform can be used to decompose a time series with respect to a set of basis functions, each one of which is associated with a particular scale. The properties of a time series at different scales can then be summarized by the wavelet variance, which decomposes the v...

Abstract. In order to get an efficient representation of images which contain orientated edges we construct a directional wavelet basis for L(R). The wavelets basis consists of Haar wavelets with compact support on triangles. In comparison with the classical wavelet transform our functions offer two more directions (diagonal directions). Applying our simple wavelet system to image denoising and...

To study the characteristics of license plate characters recognition, this paper proposes a method for feature extraction of license plate characters based on two-dimensional wavelet packet. We decompose license plate character images with two dimensional-wavelet packet and search for the optimal wavelet packet basis. This paper presents a criterion of searching for the optimal wavelet packet b...

In the present paper, we introduce theH-wavelet method for the fast solution of nonlocal operator equations on unstructured meshes. On the given mesh, we construct a wavelet basis which provides vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates is compressed to O(N logN) relevant matrix coefficients, where...

The orthonormal basis generated by a wavelet of L 2 (R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L 2 (R d) is called the multiwavelet packet basis. The concept of wavelet frame packet is also gen...

The use of high performance computers for wavelet and wavelet packet based image coding is discussed. After a short description of wavelet and wavelet packet methods the existing literature concerning vector, parallel and VLSI wavelet transforms is reviewed. In the following an algorithm for wavelet packet best basis selection on moderate parallel MIMD architectures is introduced and an impleme...

We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a uniform grid. Therefore, the wavelets have eight vanishing moments, and the matrices arising from discretization of differential equations with coeffic...