The central issue of the present note is the BLaC operator, a ”Blending of Linear and Constant” approach. Several properties are proved, e.g., its positivity and the reproduction of constant functions. Starting from these results, error estimates in terms of ω1 and ω2 are given. Furthermore, we present the degree of approximation in the bivariate tensor product case. This is applicable to image...

It has been observed from image denoising experiments that translation invariant (TI) wavelet transforms often outperform orthogonal wavelet transforms. This paper compares the two transforms from the viewpoint of approximation theory, extending previous results based on Haar wavelets. The advantages of the TI expansion over orthogonal expansion are twofold: the TI expansion produces smaller ap...

Given a complete separable nite measure space (X; ; ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp(X; ; ) where 1 < p <1. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if (X; ; ) is not purely atomic, then the unconditional basis constant of our basis is (max(p; q) 1). We derive a fast a...

This paper investigates video coding with wavelet transforms applied in the temporal direction of a video sequence. The wavelets are implemented with the lifting scheme in order to permit motion compensation between successive pictures. We generalize the coding scheme and permit motion compensation from any even picture in the GOP by maintaining the invertibility of the inter-frame transform. W...

The wavelet subspaces of the space of square integrable functions on the affine group with respect to the left invariant Haar measure dν are studied using the techniques from [9] with respect to wavelets whose Fourier transforms are related to Laguerre polynomials. The orthogonal projections onto each of these wavelet subspaces are described and explicit forms of reproducing kernels are establi...

This paper is based on [CPSSZ00] which is to appear in Experimental Mathematics. The name wavelet was made up by French researchers [MAFG82, Mor83, GM84] for a particular class of functions. The existence of wavelet-like functions has been known since the beginning of the century (a notable example is what is known as the Haar wavelet today [Haa10]). However, only recently the unifying concepts...

In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solve the obta...

Este artigo desenvolve uma metodologia numérica, utilizando conjuntamente as plataformas computacionais ANSYS® e Matlab®, para localizar quantificar danos estruturais em treliças vigas. Esses sistemas são modelados numericamente via Método dos Elementos Finitos no ANSYS®, posteriormente, o sinal (deflexão) sofrida pela estrutura é transformado Transformada Contínua de Wavelet (TW) Matlab®. A mo...

In this work, we present a computational method for solving double and triple integrals with variable limits of integrations which is based on Haar wavelets. This approach is the generalization and improvement of the methods [3]. The advantage of this new methods is its more efficient and simple applicability than the previous methods. Error analysis for the case of two dimension are considered...