In this paper, we demonstrate that image reconstruction can be expressed in terms of neural networks. We show that filtered backprojection can be mapped identically onto a deep neural network architecture. As for the case of iterative reconstruction, the straight forward realization as matrix multiplication is not feasible. Thus, we propose to compute the back-projection layer efficiently as fixed function and its gradient as projection operation. This allows a data-driven approach for joint optimization of correction steps in projection domain and image domain. As a proof of concept, we demonstrate that we are able to learn weightings and additional filter layers that consistently reduce the reconstruction error of a limited angle reconstruction by a factor of two while keeping the same computational complexity as filtered back-projection. We believe that this kind of learning approach can be extended to any common CT artifact compensation heuristic and will outperform hand-crafted artifact correction methods in the future.