A spline inversion formula for the Radon transform

An approximate inversion formula is given for the Radon Transform of a function f in an arbitrary number of dimensions. The basic idea is to consider the least-squares approximation of f in a finite element space and to transform the normal equations into equations involving Radon data. The Radon Transform of finite elements is given in terms of multivariate B-splines and error estimates are deduced in an $L^2 $ setting.