The rst part of this work describes the full set of Daubechies Wavelets with a particular emphasis on symmetric (and complex) orthonormal bases. Some properties of the associated complex scaling functions are presented in a second part. The third and last part describes a multiscale image enhancement algorithm using the phase of the complex multiresolution representation of the 2 dimension sign...

1.1 Pictures of complex wavelets Figure 1 shows the six distinct Daubechies’ wavelets with five vanishing moments. Panels (c) and (f) show respectively the familiar extremal phase and least asymmetric real wavelets, while the other panels show the four distinct complex-valued wavelets. Even though these cDws share the same number of vanishing moments, they are visually very different to each ot...

A new method to construct a Daubechies wavelets combined sparse basement based on compressed sensing theory is proposed in this paper, which is particularly suitable for the sensing signals with time correlation characteristics. In this research, the simplified dictionary is constructed by Daubechies wavelets function after atoms checking and screening. This sparse basement is obtained by the c...

We present new quantitative results for the characterization of the b-error of wavelet-like expansions as a function of the scale a. This yields an extension as well as a simplification of the asymptotic error formulas that have been published previously. We use our bound determinations to compare the approximation power of various families of wavelet transforms. We present explicit formulas fo...

We show how Daubechies wavelets are used to solve Kuramoto-Sivashinsky type equations with periodic boundary condition‎. ‎Wavelet bases are used for numerical solution of the Kuramoto-Sivashinsky type equations by Galerkin method‎. ‎The numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.    

Digital mammograms are coupled with noise which makes de-noising a challenging problem. In the literature, few wavelets like daubechies db3 and haar have been used for de-noising medical images. However, wavelet filters such as sym8, daubechies db4 and coif1 at certain level of soft and hard threshold have not been taken into account for mammogram images. Therefore, in this study five wavelet f...

It is generally accepted that self-similar (or fractal) processes may provide better models of teletraffic in modern computer networks than Poisson processes. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic selfsimilar sequences. A new generator of pseudo-random self-similar sequences, based on t...