In this paper, Semi-orthogonal (SO) B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of linear and non-linear second order Fredholm integro-differential equations. The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this functions are presented to reduce the solution of linear and...

The field of image processing deals with a major issue, i.e., the suppression of noise from the wanted images. The intention of this message is to highlight some of the unique properties of spline wavelets. In this paper image denoising is performed using simulated noise images with various characteristics with the help of semi-orthogonal spline wavelets in comparison with CDF 9/7 wavelets. B-s...

This paper presents an eecient algorithm to generate realistic images using spline wavelets. Our algorithm departs from the use of non-overlapping wavelets by providing a continuous solution at no extra cost. This in turn eliminates need for inaccurate Gouraud shading or expensive nal gather step. Advantage of spline wavelets come from the fact that scaling functions are n th order B-splines th...

The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L ...

In this paper a new digital audio watermarking algorithm is proposed based on B-spline approximation. The algorithm takes the advantage of non-uniform B-spline wavelet, namely, the number of low-frequency components can be arbitrarily selected, so, it is very flexible. Meanwhile, it avoids the complex calculations of non-uniform B-spline wavelets. The simulation experiments show that this algor...

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. 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 computationally attractive, an...

A series expansion with remainder for functions in a Sobolev space is derived in terms of the classical Bernoulli polynomials, the B-spline scale-space and the continuous wavelet transforms with the derivatives of the standardized B-splines as mother wavelets. In the limit as their orders tend to infinity, the B-splines and their derivatives converge to the Gaussian function and its derivatives...

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...

The biorthogonal wavelets introduced by Cohen, Daubechies, and Feauveau contain in particular compactly supported biorthogonal spline wavelets with compactly supported duals. We present a new approach for the construction of compactly supported spline wavelets, which is entirely based on properties of splines in the time domain. We are able to characterize a large class of such wavelets which c...