We address the issue of constructing directional wavelet bases. After considering orthonormal directional wavelets whose Fourier transforms are indicator functions, we give a construction of directional wavelets with fast decay that is based on an hexagonal filter bank tree. An implementation for squarely sampled images and numerical results are presented. Then we discuss the frequency localiza...

Wavelet-based image denoising algorithm depends upon the energy compaction property of wavelet transforms. However, for many real-world images, we cannot expect good energy compaction in a single wavelet domain, because most real-world images consist of components of a variety of smoothness. We can relieve this problem by using multiple wavelet bases to match different characteristics of images...

Some years ago, compactly supported divergence-free wavelets were constructed which also gave rise to a stable (biorthogonal) wavelet splitting of H(div; Ω). These bases have successfully been used both in the analysis and numerical treatment of the Stokes and Navier–Stokes equations. In this paper, we construct stable wavelet bases for the stream function spaces H(curl; Ω). Moreover, curl-free...

Wavelet packet transform decomposes a signal into a set of orthonormal bases (nodes) and provides opportunities to select an appropriate set of these bases for feature extraction. In this paper, multi-level basis selection (MLBS) is proposed to preserve the most informative bases of a wavelet packet decomposition tree through removing less informative bases by applying three exclusion criteria:...

In this paper, a new image synthesis model based on a set of wavelet bases is proposed. In the proposed model, images are approximated by the sum of synthesis functions that are translated to image edge positions. By applying the proposed model to sketch-based image coding, no iterative image recovery procedure is required for image decoding. In the design of the synthesis functions, we define ...

In this correspondence, we generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M -channel. A sufficient condition for the M -channel perfect reconstruction filter banks to constructM -channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M -channel wavelet bases is equivalent to the design of a...

A new progressive transmission scheme using spline biorthogorial wavelet bases is proposed in this paper: First, several wavelet bases are compared with the spline biorthogo-nul nmvlet bases. By exploiting the properties of this set of wuvelet bases, a fast algorithm involving only additions and subtruc.tintts is developed. Due to the multiresolutional nature cf the wavelet transform. this sche...

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.    

In both applications and wavelet theory, the spline wavelets are especially interesting, in part because of their simple structure. In a previous paper we proved that the function m;l is an m th order spline wavelet having an l th order spline dual wavelet. This enabled us to derive biorthogonal spline wavelet bases. In this paper we rst study the general structure of cardinal spline wavelets, ...

In this paper, redundant bases for denoising are constructed completely in the frequency-domain. The advantage of the frequency-domain bases construction approach is that it provides much more flexibility. As a result, the filterbank (basis) can be constructed to fit the features of the signal more closely, and the filter’s frequency response in the filterbank can be designed to be very close t...