  Traditional model-based image reconstruction (MBIR) methods combine forward
and noise models with simple object priors. Recent machine learning methods for
image reconstruction typically involve supervised learning or unsupervised
learning, both of which have their advantages and disadvantages. In this work,
we propose a unified supervised-unsupervised (SUPER) learning framework for
X-ray computed tomography (CT) image reconstruction. The proposed learning
formulation combines both unsupervised learning-based priors (or even simple
analytical priors) together with (supervised) deep network-based priors in a
unified MBIR framework based on a fixed point iteration analysis. The proposed
training algorithm is also an approximate scheme for a bilevel supervised
training optimization problem, wherein the network-based regularizer in the
lower-level MBIR problem is optimized using an upper-level reconstruction loss.
The training problem is optimized by alternating between updating the network
weights and iteratively updating the reconstructions based on those weights. We
demonstrate the learned SUPER models' efficacy for low-dose CT image
reconstruction, for which we use the NIH AAPM Mayo Clinic Low Dose CT Grand
Challenge dataset for training and testing. In our experiments, we studied
different combinations of supervised deep network priors and unsupervised
learning-based or analytical priors. Both numerical and visual results show the
superiority of the proposed unified SUPER methods over standalone supervised
learning-based methods, iterative MBIR methods, and variations of SUPER
obtained via ablation studies. We also show that the proposed algorithm
converges rapidly in practice.
