Computerized tomography requires suitable numerical methods for the approximation of a bivariate
function f from a finite set of discrete Radon data, each of whose data samples represents one line
integral of f . In standard reconstruction methods, specific assumptions concerning the geometry
of the Radon lines are usually made. In relevant applications of image reconstruction, however,
such assumptions are often too restrictive. In this case, one would rather prefer to work with
reconstruction methods allowing for arbitrary distributions of scattered Radon lines.
This paper proposes a novel image reconstruction method for scattered Radon data, which combines
kernel-based scattered data approximation with a well-adapted regularization of the Radon transform.
This results in a very flexible numerical algorithm for image reconstruction, which works for arbitrary
distributions of Radon lines. This is in contrast to the classical filtered back projection, which
essentially relies on a regular distribution of the Radon lines, e.g. parallel beam geometry. The good
performance of the kernel-based image reconstruction method is illustrated by numerical examples
and comparisons