  Computed Tomography (CT) is a prominent example of Imaging Inverse Problem
highlighting the unrivaled performances of data-driven methods in degraded
measurements setups like sparse X-ray projections. Although a significant
proportion of deep learning approaches benefit from large supervised datasets,
they cannot generalize to new experimental setups. In contrast, fully
unsupervised techniques, most notably using score-based generative models, have
recently demonstrated similar or better performances compared to supervised
approaches while being flexible at test time. However, their use cases are
limited as they need considerable amounts of training data to have good
generalization properties. Another unsupervised approach taking advantage of
the implicit natural bias of deep convolutional networks, Deep Image Prior, has
recently been adapted to solve sparse CT by reparameterizing the reconstruction
problem. Although this methodology does not require any training dataset, it
enforces a weaker prior on the reconstructions when compared to data-driven
methods. To fill the gap between these two strategies, we propose an
unsupervised conditional approach to the Generative Latent Optimization
framework (cGLO). Similarly to DIP, without any training dataset, cGLO benefits
from the structural bias of a decoder network. However, the prior is further
reinforced as the effect of a likelihood objective shared between multiple
slices being reconstructed simultaneously through the same decoder network. In
addition, the parameters of the decoder may be initialized on an unsupervised,
and eventually very small, training dataset to enhance the reconstruction. The
resulting approach is tested on full-dose sparse-view CT using multiple
training dataset sizes and varying numbers of viewing angles.
