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...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

in this paper, we present an edge detection method based on wavelet transform and hessian matrix of image at each pixel. many methods which based on wavelet transform, use wavelet transform to approximate the gradient of image and detect edges by searching the modulus maximum of gradient vectors. in our scheme, we use wavelet transform to approximate hessian matrix of image at each pixel, too. ...

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

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...