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size: 7,935 bytes

date: 19.07.2012

Symmetric Exponential B-spline

Hagai Kirshner, Biomedical Imaging Group, EPFL.


This collection of Matlab functions calculate symmetric exponential splines. In particular, they compute the values of a Sobolev space reproducing kernel, which is also the autocorrelation of an ARMA process. The functions also compute the values of the corresponding B-spline and the associated interpolation function.

The files are:

An example of exponential splines. The reproducing kernel φ(t) has a rational Laplace transform, and the coefficients of its polynomials provide the parameterization of the spline. Shown here is the reproducing kernel of a Sobolev space that has three poles (-1-i, -1+i, -1). The function β(t) is the associated B-spline and ψ(t) is the interpolation function


H. Kirshner, S. Maggio, M. Unser, "A Sampling Theory Approach for Continuous ARMA Identification," IEEE Transactions on Signal Processing, vol. 59, no. 10, pp. 4620-4634, October 2011

H. Kirshner, M. Porat, "On the Role of Exponential Splines in Image Interpolation," IEEE Transactions on Image Processing, vol. 18, no. 10, pp. 2198-2208, October 2009

Terms of use

The software is freely available for research purposes.

One needs to have our consent before transmitting and/or distributing it further on.

Presented and/or published material that is based on this software should include the relevant citation.

The EPFL makes no warranties of any kind on this software and shall in no event be liable for damages of any kind in connection with the use and exploitation of this technology.