Wendland radial basis functions applied as filters on computed tomography

Wendland radial basis functions are applied as an alternative solution to the interpolation problem when the filtered back projection algorithm is used in computed tomography. Since we have a regular grid of data points and these functions are compactly supported, the interpolation can be made as a fast filtering process rather than solving a typical linear system of equations. This allows us to apply the Error Kernel method, which gives details of the approximation quality in the frequency domain, when we make interpolation with basis functions such as the B-splines. The Error Kernel provides us a direct comparison between Wendland functions and B-splines. The comparison shows that the Wendland functions can offer the same interpolation quality of the B-splines when the support is large, but with a small support the performance is poor. We see this behavior making tomographic reconstructions with different Wendland functions and also with different supports. A numerical experiment consisting of successive image rotations to an image was performed to verify the similarities between the Wendland functions and B-splines.