Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.

We generalize the exponential box spline by allowing it to have arbitrarily spaced knots in any of its directions and derive the corresponding recurrence and differentiation rules. The corresponding spline space is spanned by the shifts of finitely many such splines and contains the usual family of exponential polynomials. The (local) linear independence of the spanning set is equivalent to a g...

Cardiovascular magnetic resonance (CMR) perfusion data are suitable for quantitative measurement of myocardial blood flow. The goal of perfusionCMR postprocessing is to recover tissue impulse-response from observed signalintensity curves. While several deconvolution techniques are available for this purpose, all of them use models with varying parameters for the representation of the impulse-re...

In this paper an algorithm for multi-color image compression-encryption is introduced. For compression step fuzzy transform based on exponential b-spline function is used. In encryption step, a novel combination chaotic system based on Sine and Tent systems is proposed. Also in the encryption algorithm, 3D shift based on chaotic system is introduced. The simulation results and security analysis...

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...

in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...

The subject of this investigation is the class of difference functionals—linear combinations of finitely many function and/or derivative evaluations—which annihilate the nullspace of a certain constant coefficient differential operator. Any such functional can be viewed as an integral-differential operator whose Peano kernel is a compactly supported exponential spline. Besides extending some ea...

Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...