Glossary 5 Introduction 6 Definition of Wavelets 7 Definition of Filters 8 Multi-Resolution Analysis 9 Wavelet Decomposition and Reconstruction 10 Refinable Functions 11 Compactly Supported Orthonormal Wavelets 12 Parameterization of Orthonormal Wavelets 13 Biorthogonal Wavelets 14 Prewavelets 15 Tight Wavelet Frames 16 Tight Wavelet Frames over Bounded Domain 17 q-Dilated Orthonormal Wavelets ...

In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.

Chui and Wang discussed the construction of one-dimensional compactly supported wavelets under a general framework, and constructed one-dimensional compactly supported spline wavelets. In this paper, under a mild condition, the construction of M = ( 1 1 1 −1 )-wavelets is obtained.

Glossary 5 Introduction 6 Definition of the Subject 7 Various Spline Spaces 8 The B-form Representation of Spline Functions 9 Dimension of Multivariate Spline Spaces 10 Approximation Power of Spline Spaces 11 Construction of Finite Elements 12 and Macro-Elements 13 Multivariate Splines for Scattered Data Fitting 14 Multivariate Splines for Numerical Solution 15 of Partial Differential Equations...

We generalize earlier results concerning an asymptotic error expansion of wavelet approximations. The properties of the monowavelets, which are the building blocks for the error expansion, are studied in more detail, and connections between spline wavelets and Euler and Bernoulli polynomials are pointed out. The expansion is used to compare the error for different wavelet families. We prove tha...

We construct biorthogonal spline wavelets for periodic splines which extend the notion of “lazy” wavelets for linear functions (where the wavelets are simply a subset of the scaling functions) to splines of higher degree. We then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight fun...

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...

l j l ZZ r g Then r are called orthogonal wavelets of multiplicity r if B forms an orthonormal basis of L IR We say that r are wavelets prewavelets of multiplicity r if B forms a Riesz basis of L IR and j l is orthogonal to k n f r g l n j k ZZ with j k The general theory of wavelets of multiplicity r is treated in As usual the method is based on a generalization of the notion of multiresolutio...

In this study, an effective technique upon compactly supported semi orthogonal cubic Bspline wavelets for solving nonlinear Volterra-Fredholm integral equations is proposed. Properties of B-spline wavelets and function approximation by them are first presented and the exponential convergence rate of the approximation, Ο(2 -4j ), is proved. For solving the nonlinear Volterra-Fredholm integral eq...