On the n-dimensional hypercube, for given k ∈ N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual wavelets can be constructed to be locally supported. The construction of the isotropic wavelet ...

The WSO M (Wavelet SelfOrganizing 1\Jap) model, a rwural network for the erea.tion of wavelet bases adapted to the distribution of input data, is introduced. The model provides an efficient on-lim) way to construct high-dimensional wavelet bases. Simulations of a lD function approximation problem illustrate how WSOM adapts to non-uniformly distributed input data, outperforming the discrete wa.v...

On the n-dimensional hypercube, for given k ∈ N, biorthogonal wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and dual wavelets can be constructed to be locally supported. The construction of the isotropic wave...

In this paper, we propose a texture feature extraction scheme at multiple scales and discuss the issues of rotation and gray-scale transform invariance as well as noise tolerance of a texture analysis system. The nonseparable discrete wavelet frame analysis is employed which gives an overcomplete wavelet decomposition of the image. The texture is decomposed into a set of frequency channels by a...

A new progressive transmission scheme using spline biorthogonal wavelet bases is proposed in this paper. First, several wavelet bases are compared with the spline biorthogo-nal wavelet bases. By exploiting the properties of this set of wavelet bases, a fast algorithm involving only additions and subtractions is developed. Due to the multiresolutional nature of the wavelet transform, this scheme...

This paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order. Because multiwavelet bases normally lack important properties that traditional wavelet bases (of equal approximation order) possess, the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step (prefiltering...

The existence in L2(R) of biorthogonal wavelet bases associated with perfect reconstruction 2 channel filter banks comprising finite, real filters is determined by the eigenvalues of two related Lawton matrices. Each Lawton matrix is required to have a simple eigenvalue at one and all remaining eigenvalues must have modulus less than one. This being the case then the wavelet bases are said to b...

We use special functions and orthonormal wavelet bases on the real line to construct wavelet-like bases. With these wavelets we can construct polynomial bases on the interval; moreover, we can use them for the numerical resolution of degenerate elliptic operators.