  Model-based learned iterative reconstruction methods have recently been shown
to outperform classical reconstruction algorithms. Applicability of these
methods to large scale inverse problems is however limited by the available
memory for training and extensive training times, the latter due to
computationally expensive forward models. As a possible solution to these
restrictions we propose a multi-scale learned iterative reconstruction scheme
that computes iterates on discretisations of increasing resolution. This
procedure does not only reduce memory requirements, it also considerably speeds
up reconstruction and training times, but most importantly is scalable to large
scale inverse problems with non-trivial forward operators, such as those that
arise in many 3D tomographic applications. In particular, we propose a hybrid
network that combines the multi-scale iterative approach with a particularly
expressive network architecture which in combination exhibits excellent
scalability in 3D.
  Applicability of the algorithm is demonstrated for 3D cone beam computed
tomography from real measurement data of an organic phantom. Additionally, we
examine scalability and reconstruction quality in comparison to established
learned reconstruction methods in two dimensions for low dose computed
tomography on human phantoms.
