Irregular Sampling and the Radon Transform

In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling and interpolation methods. This article presents one approach to the inversion of the Radon transform that uses a discrete set of samples which need not be completely regular. This approach is based on a sampling theorem that employs fundamental solutions of an elliptic differential operator D .