  We introduce the learned simultaneous iterative reconstruction technique
(SIRT) for tomographic reconstruction. The learned SIRT algorithm is a deep
learning based reconstruction method combining model knowledge with a learned
component. The algorithm is trained by mapping raw measured data to the
reconstruction results over several iterations. The Learned SIRT algorithm is
applied to a cone beam geometry on a circular orbit, a challenging problem for
learned methods due to its 3D geometry and its inherent inability to completely
capture the patient anatomy. A comparison of 2D reconstructions is shown, where
the learned SIRT approach produces reconstructions with superior peak signal to
noise ratio (PSNR) and structural similarity (SSIM), compared to FBP, SIRT and
U-net post-processing and similar PSNR and SSIM compared to the learned primal
dual algorithm. Similar results are shown for cone beam geometry
reconstructions of a 3D Shepp Logan phantom, where we obtain between 9.9 and
28.1 dB improvement over FBP with a substantial improvement in SSIM. Finally we
show that our algorithm scales to clinically relevant problems, and performs
well when applied to measurements of a physical phantom.
