  Tomographic image reconstruction is relevant for many medical imaging
modalities including X-ray, ultrasound (US) computed tomography (CT) and
photoacoustics, for which the access to full angular range tomographic
projections might be not available in clinical practice due to physical or time
constraints. Reconstruction from incomplete data in low signal-to-noise ratio
regime is a challenging and ill-posed inverse problem that usually leads to
unsatisfactory image quality. While informative image priors may be learned
using generic deep neural network architectures, the artefacts caused by an
ill-conditioned design matrix often have global spatial support and cannot be
efficiently filtered out by means of convolutions. In this paper we propose to
learn an inverse mapping in an end-to-end fashion via unrolling optimization
iterations of a prototypical reconstruction algorithm. We herein introduce a
network architecture that performs filtering jointly in both sinogram and
spatial domains. To efficiently train such deep network we propose a novel
regularization approach based on deep exponential weighting. Experiments on US
and X-ray CT data show that our proposed method is qualitatively and
quantitatively superior to conventional non-linear reconstruction methods as
well as state-of-the-art deep networks for image reconstruction. Fast inference
time of the proposed algorithm allows for sophisticated reconstructions in
real-time critical settings, demonstrated with US SoS imaging of an ex vivo
bovine phantom.
