A method for designing more regular (more diieren-tiable) scaling functions than the Daubechies wavelets is presented. The approach is to numerically minimize the HH older exponent (a measure of smoothness) subject to constraints on the autocorrelation sequence of the scaling lter. The \maximally smooth" wavelets which result have a HH older exponent which grows faster than that of the Daubechi...

The Coifman wavelets created by Daubechies have more zero moments than imposed by specifications. This results in systems with approximately equal numbers of zero scaling function and wavelet moments and gives a partitioning of the systems into three well defined classes. The nonunique solutions are more complex than for Daubechies wavelets.

Although the details are more complicated in two dimensions, the basic ideas behind (1) and (2) are the same: a function is described in terms of scaled and shifted copies of the “building blocks” and . More details can be found in (e.g.) Vidakovic (1999). The two families of compactly supported wavelets described by Daubechies (1992) are by far the most commonly used. These “extremal phase” an...

In this paper, we present comparative analysis of scale-invariant feature extraction using different wavelet bases. The main advantage of the wavelet transform is the multi-resolution analysis. Furthermore, wavelets enable localization in both space and frequency domains and high-frequency salient feature detection. Wavelet transforms can use various basis functions. This research aims at compa...

In the last decade, Daubechies orthogonal wavelets have been successfully used and proved their practicality in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. I...

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9/7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. We consider a dual pair of such multiresolutions, where the scaling functi...

|The magnitude of the lters associated with Daubechies' wavelets is shown to converge to an ideal high-pass lter when the length of the support of the wavelets increases to 1. The convergence of the lters is monotonic. That is, the larger support of a Daubechies' wavelet, the better quality of the lter associated with. The rate of the convergence is also given. The magnitude of the lter associa...

Analyses based on Symmetric Daubechies Wavelets (SDW) lead to complex-valued multiresolution representations of real signals. After a recall of the construction of the SDW, we present some speciic properties of these new types of Daubechies wavelets. We then discuss two applications in image processing: enhancement and restoration. In both cases, the eeciency of this multiscale representation r...

Wavelet transforms for discrete-time periodic signals are developed. In this nite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies, and Feauveau are isolated to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported wavelets. These discrete-time periodic...