  The performance of an iterative reconstruction algorithm for X-ray tomography
is strongly determined by the features of the used forward and backprojector.
For this reason, a large number of studies has focused on the to design of
projectors with increasingly higher accuracy and speed. To what extent the
accuracy of an iterative algorithm is affected by the mathematical affinity and
the similarity between the actual implementation of the forward and
backprojection, referred here as "coupling projector-backprojector", has been
an overlooked aspect so far. The experimental study presented here shows that
the reconstruction quality and the convergence of an iterative algorithm
greatly rely on a good matching between the implementation of the tomographic
operators. In comparison, other aspects like the accuracy of the standalone
operators, the usage of physical constraints or the choice of stopping criteria
may even play a less relevant role.
