  In numerous practical applications, especially in medical image
reconstruction, it is often infeasible to obtain a large ensemble of
ground-truth/measurement pairs for supervised learning. Therefore, it is
imperative to develop unsupervised learning protocols that are competitive with
supervised approaches in performance. Motivated by the maximum-likelihood
principle, we propose an unsupervised learning framework for solving ill-posed
inverse problems. Instead of seeking pixel-wise proximity between the
reconstructed and the ground-truth images, the proposed approach learns an
iterative reconstruction network whose output matches the ground-truth in
distribution. Considering tomographic reconstruction as an application, we
demonstrate that the proposed unsupervised approach not only performs on par
with its supervised variant in terms of objective quality measures but also
successfully circumvents the issue of over-smoothing that supervised approaches
tend to suffer from. The improvement in reconstruction quality comes at the
expense of higher training complexity, but, once trained, the reconstruction
time remains the same as its supervised counterpart.
