  Nowadays, the field computed tomography (CT) encompasses a large variety of
settings, ranging from nanoscale to meter-sized objects imaged by different
kinds of radiation in various acquisition modes. This experimental diversity
challenges the flexibility of tomographic reconstruction methods. Kaczmarz-type
methods, which exploit the natural block-structure of tomographic inverse
problems, are a promising candidate to provide the required versatility in a
computationally efficient manner. In the present work, it is shown that indeed
a surprisingly general class of tomographic Kaczmarz-iterations may be
efficiently evaluated via computational schemes of a similar structure as
updates of the so-called simultaneous algebraic reconstruction technique
(SART). This enables regularized reconstructions with non-trivial
image-formation models as well as non-quadratic or even non-convex
data-fidelity terms at low computational costs. Moreover, the proposed
generalized SART schemes are equally applicable in parallel- and cone-beam
settings and regardless of the choice of tomographic incident directions. Their
potential is illustrated by outlining applications in several non-standard
tomographic settings, including polychromatic CT and X-ray phase contrast
tomography.
