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.

翻译：计算机断层扫描（CT）是成像逆问题的一个典型实例，突显了数据驱动方法在稀疏X射线投影等退化测量设置中的卓越性能。尽管大多数深度学习方法受益于大规模监督数据集，但它们无法泛化到新的实验设置。相比之下，完全无监督技术（最显著的是基于评分生成模型）最近在测试时展现出与监督方法相当甚至更优的性能，同时保持灵活性。然而，其应用场景受限，因为需要大量训练数据才能具备良好的泛化特性。另一种利用深度卷积网络隐式自然偏差的无监督方法——深度图像先验（Deep Image Prior），最近通过重参数化重建问题被适配用于解决稀疏CT。尽管该方法无需任何训练数据集，但与数据驱动方法相比，其对重建施加的先验约束较弱。为填补这两种策略之间的空白，我们提出了一种面向生成式潜在优化框架的无监督条件方法（cGLO）。与DIP类似，cGLO无需训练数据集即可受益于解码器网络的结构偏差。然而，由于多个切片通过同一解码器网络同时重建时共享似然目标，其先验约束得到进一步增强。此外，解码器参数可在无监督（甚至极小规模）训练数据集上初始化，以提升重建效果。所提方法在多个训练数据集规模和不同视角数下，基于全剂量稀疏视角CT进行了验证。