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.

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