  Photon-counting CT (PCCT) offers improved diagnostic performance through
better spatial and energy resolution, but developing high-quality image
reconstruction methods that can deal with these large datasets is challenging.
  Model-based solutions incorporate models of the physical acquisition in order
to reconstruct more accurate images, but are dependent on an accurate forward
operator and present difficulties with finding good regularization. Another
approach is deep-learning reconstruction, which has shown great promise in CT.
However, fully data-driven solutions typically need large amounts of training
data and lack interpretability. To combine the benefits of both methods, while
minimizing their respective drawbacks, it is desirable to develop
reconstruction algorithms that combine both model-based and data-driven
approaches. In this work, we present a novel deep-learning solution for
material decomposition in PCCT, based on an unrolled/unfolded iterative
network. We evaluate two cases: a learned post-processing, which implicitly
utilizes model knowledge, and a learned gradient-descent, which has explicit
model-based components in the architecture. With our proposed techniques, we
solve a challenging PCCT simulation case: three-material decomposition in
abdomen imaging with low dose, iodine contrast, and a very small training
sample support. In this scenario, our approach outperforms a maximum likelihood
estimation, a variational method, as well as a fully-learned network.
