Abstract. Given a biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, we build a new biorthogonal pair of multiresolution analyses. Using both pairs, isotropic or, as we focus on, anisotropic divergence-free wavelet bases on the hypercube are constructed. Our construction generalizes the one from [Rev. Mat. Iberoamericana, 8 (1992), pp. 221–237] by...

We will be concerned with the solution of an elliptic boundary value problem in one dimension with polynomial coeecients. In a Galerkin approach, we employ biorthogonal wavelets adapted to a diierential operator with constant coeecients, and use the reenement equations to set up the system of linear equations with exact entries (up to round-oo). For the solution of the linear equation, we const...

This paper first shows that the Cohen-Daubechies-Feauveau (C-D-F) biorthogonal wavelet can be derived from the interpolating wavelet through a lifting process. Its high-pass filter measures the interpolation error of the averaged data. Next, we propose a new wavelet method, called the difference wavelet method, for efficient representation for functions on R. Its analysis part is simply averagi...

We show that a multi-dimensional scaling function of order γ (possibly fractional) can always be represented as the convolution of a polyharmonic B-spline of order γ and a distribution with a bounded Fourier transform which has neither order nor smoothness. The presence of the B-spline convolution factor explains all key wavelet properties: order of approximation, reproduction of polynomials, v...

Wavelet techniques have achieved a tremendous success in image data compression. In designing wavelet coding algorithms, the choice of wavelet systems is of great importance for compression performance. In this paper, we design the entire class of antisymmetric biorthogonal coiiet systems, whose l-terbanks have even lengths and are linear phase. We show that one of the novel lterbanks achieves ...

In the present work we analyze the performance of orthogonal and Biorthogonal wavelet filters for image compression on variety of test images. The test images are of different size and resolution. The compression performance is measured, objectively peak signal to noise ratio and subjectively visual quality of image and it is found that Biorthogonal wavelets outperform the orthogonal ones in bo...

Roger L. Claypoole, Jr. and Richard G. Baraniuk, Rice University Summary We introduce and discuss biorthogonal wavelet transforms using the lifting construction. The lifting construction exploits a spatial{domain, prediction{error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We discuss the application of lifting to adaptive and n...

We study the mean size of wavelet packets in Lp. An exact formula for the mean size is given in terms of the p-norm joint spectral radius. This will be a corollary of an asymptotic formula for the Lp-norms on the subdivision trees. Then the stability and Schauder basis property of wavelet packets in Lp, and the instability of biorthogonal wavelet packets in L2 are analyzed. AMS Subject Classifi...

This is the first part of our two papers in which we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. We give extension of our previous results to the case of periodic orbital particle motion in ...