  This paper presents a novel mathematical framework for understanding
pixel-driven approaches for the parallel beam Radon transform as well as for
the fanbeam transform, showing that with the correct discretization strategy,
convergence - including rates - in the $L^2$ operator norm can be obtained.
These rates inform about suitable strategies for discretization of the
occurring domains/variables, and are first established for the Radon transform.
In particular, discretizing the detector in the same magnitude as the image
pixels (which is standard practice) might not be ideal and in fact,
asymptotically smaller pixels than detectors lead to convergence. Possible
adjustments to limited-angle and sparse-angle Radon transforms are discussed,
and similar convergence results are shown. In the same vein, convergence
results are readily extended to a novel pixel-driven approach to the fanbeam
transform. Numerical aspects of the discretization scheme are discussed, and it
is shown in particular that with the correct discretization strategy, the
typical high-frequency artifacts can be avoided.
