In this article, we utilize spline wavelets to establish an adaptive multilevel numerical scheme for timedependent convection-dominated diffusion problems within the frameworks of Galerkin formulation and Eulerian-Lagrangian localized adjoint methods (ELLAM). In particular, we shall use linear Chui-Quak semiorthogonal wavelets, which have explicit expressions and compact supports. Therefore, bo...

While it is well known that the mth order 5-spline Nm(x) with integer knots generates a multiresolution analysis, • • • C V_x c V0 C • ■ • , with the with order of approximation, we prove that i//(x) := Ú1mJ¡{2x 1), where L2m(x) denotes the (2m)th order fundamental cardinal interpolatory spline, generates the orthogonal complementary wavelet spaces Wk . Note that for m = 1 , when the ß-spline N...

Wavelets can be thought of as a set of well-localized basis functions with very good approximation properties. The diiculty in applying wavelet approximation to high-dimensional data is that the number of basis functions increases exponentially with the number of dimensions, making the application of standard mathematical methods for determining coeecients diic ult. We propose a modeling method...

In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in ...

In this work, we present a new low memory requirement and low computational time method for solving a class of integral equation of the second kind which is based on the use of B-Spline wavelets. Because of vanishing moments and compact support and semiorthogonality properties of these wavelets, operational matrix of the method is very sparse. Also, applying some appropriate thresholding parame...

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9/7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. We consider a dual pair of such multiresolutions, where the scaling functi...

While there are many possible choice of wavelets, splines have some clear advantages for biomedical imaging. First, unlike most other wavelet bases, they provide a continuous image representation that is easily computable at any spatial location — this property is crucial for implementing geometrical transformations. Second, they have the best approximation properties among all popular wavelet ...

This paper describes an approach to using compactly supported spline wavelets to model the residual signal in a real-time (frameby-frame) spectral modelling system. The outputs of the model are time-varying parameters (gain, centre frequency and bandwidth) for filters which can be used in a subtractive resynthesis system.

Wavelet-based analysis versus Gaussian smoothing in statistical parametric mapping (SPM) for detecting and analyzing brain activity from functional magnetic resonance imaging (fMRI) data is presented. Detection of activation in fMRI data can be performed in the wavelet domain by a coefficient-wise statistical t-test. The link between the wavelet analysis and SPM is based on two observations: (i...

In this work, a computational method for solving nonlinear Volterra-Fredholm-Hammerestein integral equations is proposed. Compactly supported semiorthogonal cubic B-spline wavelets are employed as basis functions then collocation method is utilized to reduce the computation of integral equations to some algebraic system. The method is computationally attractive, and applications are demonstrate...