In this paper we use the lifting scheme to construct biorthogonal spline wavelet bases on regularly refined non-uniform grids. The wavelets have at least one vanishing moment and on each resolution level they form an L2 Riesz basis. Furthermore we are interested in determining the exact range of Sobolev exponents for which the complete multilevel system forms a Riesz basis. Hereto we need to ex...

This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach ...

In this paper we consider polynomial splines with equidistant nodes which may grow as O|x|. We present an integral representation of such splines with a distribution kernel where exponential splines are used as basic functions. By this means we characterize splines possessing the property that translations of any such spline form a basis of corresponding spline space. It is shown that any such ...

In this paper, the linear semiorthogonal compactly supported B-spline wavelets together with their dual wavelets have been applied to approximate the solutions of Fredholm integral equations of the second kind. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computatio...

We propose that multiview wavelets can be used in processing multiview images. The reference functions for the synthesis/analysis of multiview images are described. The synthesized binary images were observed experimentally as three-dimensional visual images. The symmetric multiview B-spline wavelets are proposed. The locations recognized in the continuous wavelet transform correspond to the la...

R. Mutihac Electricity and Biophysics, University of Bucharest, Bucharest, Romania Objective Analysis of an fMRI block-based visual stimulation paradigm was comparatively performed by wavelet analysis and statistical parametric mapping (SPM) [1] based on Gaussian Random Field Theory (RFT). The voxels were isotropic and the same general linear model (GLM) was employed in both SPM and the discret...

Abstract – This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FFWavelets) including FF-Haar and FFDaubechies are derived. Non-orthogonal FFwavelets such as B-spline over GF(p) are also considered. A few examples of multiresolution analysis over Finite fields are presented showing how to perform Laplacian pyramid filtering of finite ...