Most physical systems are inevitably affected by uncertainties due to natural variabili-ties or incomplete knowledge about their governing laws. To achieve predictive computer simulations of such systems, a major task is, therefore, to study the impact of these uncertainties on response quantities of interest. Within the probabilistic framework, uncertainties may be represented in the form of r...

Given a pair of biorthogonal, compactly supported multiwavelets, we present an algorithm for raising their approximation orders to any desired level, using one lifting step and one dual lifting step. Free parameters in the algorithm are explicitly identified, and can be used to optimize the result with respect to other criteria.

A multiresolution solver is presented for all-electron Hartree-Fock and Kohn-Sham equations for general polyatomic molecules. The distinguishing features of our numerical solver are that the basis error is eliminated within a user-specified precision, the computational cost of applying operators scales linearly with the number of parameters in a correct physical sense, and the equations are sol...

Transition metal-catalyzed reactions invariably include steps where ligands associate or dissociate. In order to obtain reliable energies for such reactions, sufficiently large basis sets need be employed. this paper, we have used high-precision multiwavelet calculations compute the metal–ligand association 27 transition metal complexes with common ligands, as H2, CO, olefins, and solvent molec...

The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data [1,2]. Multiwavelets, wavelets with several scaling functions, have recently been introduced and they offer simultaneous orthogonality, symmetry and short support; which is not possible with ordinary wavelets, also called scalar wavelets [3]. This property makes multiwa...

R.Sumalatha, M.V.Subramanyam Abstract— In this paper we propose an efficient region of interest (ROI) coding technique based on multiwavelet transform, set partitioning in hierarchial (SPIHT) algorithm of medical images. This new method reduces the importance of background coefficients in the ROI code block without compromising algorithm complexity. By using this coding method the compressed bi...

In this paper, we attempt to develop image watermarking algorithms which are portable to a variety of applications such as copyright protection, fingerprinting and identification. Therefore, we require that the watermark be binary and be not only detectable but also extractable. The embedding technique is based on the parent-child structure of the multiwavelet transform called " triple tree " a...

In this article, we discuss wavelet versions of nonparametric curve estimators and weighted least squares wavelet regression. We introduce a modi ̄ed wavelet version of the Gasser-MÄ uller estimator that is unbiased whenever a wavelet representation of the nonparametric response curve correctly speci ̄es the response. In some cases, involving the Daubechies wavelet system, we ̄nd that the modi ̄ed ...