With respect to space-time tensor-product wavelet bases, parabolic initial boundary value problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet methods are shown to yield sequences of approximate solutions which converge at the optimal rate. In case the spatial domain is of product type, the use of spatial tensor product wavelet bases is proved to overcome the so...

This paper presents an algebraic approach to construct Mband orthogonal wavelet bases. A system of constraint equations is obtained for M-band orthonormal filters, and then a solution based on SVD (Singular Value Decomposition) is developed to enable us to produce innumerable wavelet bases of given length. Also the property of 2 vanishing moments is integrated into our wavelet construction proc...

This paper is concerned with the construction of biorthogonal wavelet bases on n-dimensional cubes which provide Riesz bases for Sobolev and Besov spaces with homogeneous Dirichlet boundary conditions on part of the boundary. The essential point is that the primal and dual wavelets satisfy certain corresponding complementary boundary conditions. These results form the key ingredients of the con...

In the present paper, we study nonlinear approximation properties of multivariate wavelet biframes. For a certain range of parameters, the approximation classes associated with best N term approximation are determined to be Besov spaces and thresholding the wavelet bi-frame expansion realizes the approximation rate. Our findings extend results about dyadic wavelets to more general scalings. Fin...

The application of the wavelet transform in image processing is most frequently based on a separable construction. While simple, such an approach is not capable of capturing properly all 2D properties in images. In this paper, a new truly separable multidirectional transform is proposed with a subsampling method based on lattice theory. Applications are possible in many areas of image processin...

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...

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.