In this paper, we propose the cubic semi-orthogonal compactly supported B-spline wavelets as a basis functions for the efficient solution of the second kind Fredholm integral equations system. Properties of these wavelets first presented and these properties are then used to reduce the computation of system of integral equations to some algebraic equations. The exponential convergence rate of t...

This paper presents an alternative to the semi-orthogonal spline wavelets classically used for multiresolution representation in the eld of computer aided design. This new approach involves less computation, is more modular, and is potentially more exible than the classical approach. This multiresolution scheme is presented through the use of HB-splines, a speciic subset of particular B-splines...

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

Battle-Lemarié’s wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to `. The passing and stopping bands of the ideal filter are depende...

It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg’s uncertainty principle. In this thesis, we address the construction of complex wavelets modeled on the Gabor function, and smoothing kernels based on the Gaussian. We procee...

Approximation, B-Splines, Geometry Compression, Lifting, Subdivision Surfaces, Tessellations, Wavelets We present a new construction approach for symmetric lifted B-spline wavelets on irregular polygonal control meshes defining two-manifold topologies. Polygonal control meshes are recursively refined by stationary subdivision rules and converge to piecewise polynomial limit surfaces. At every s...

The notion of tight (wavelet) frames could be viewed as a generalization of orthonormal wavelets. By allowing redundancy, we gain the necessary flexibility to achieve such properties as “symmetry” for compactly supported wavelets and, more importantly, to be able to extend the classical theory of spline functions with arbitrary knots to a new theory of spline-wavelets that possess such importan...

Tomographic reconstruction from PET data is an ill-posed problem that requires regularization. Recently, Daubechies et al. [1] proposed an l (1) regularization of the wavelet coefficients that can be optimized using iterative thresholding schemes. In this paper, we extend this approach for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using classical wavelets in the tempo...