Computed Tomography (CT) is a prominent example of Imaging Inverse Problem (IIP), highlighting the unrivalled 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 to directly map experimental measurements to medical scans, they cannot generalize to unknown acquisition setups. In contrast, fully unsupervised techniques, most notably using score-based generative models, have recently demonstrated similar or better performances compared to supervised approaches to solve IIPs while being flexible at test time regarding the imaging setup. However, their use cases are limited by two factors: (a) they need considerable amounts of training data to have good generalization properties and (b) they require a backward operator, like Filtered-Back-Projection in the case of CT, to condition the learned prior distribution of medical scans to experimental measurements. To overcome these issues, we propose an unsupervised conditional approach to the Generative Latent Optimization framework (cGLO), in which the parameters of a decoder network are initialized on an unsupervised dataset. The decoder is then used for reconstruction purposes, by performing Generative Latent Optimization with a loss function directly comparing simulated measurements from proposed reconstructions to experimental measurements. The resulting approach, tested on sparse-view CT using multiple training dataset sizes, demonstrates better reconstruction quality compared to state-of-the-art score-based strategies in most data regimes and shows an increasing performance advantage for smaller training datasets and reduced projection angles. Furthermore, cGLO does not require any backward operator and could expand use cases even to non-linear IIPs.

翻译：计算机断层扫描（CT）是成像逆问题（IIP）的典型范例，凸显了数据驱动方法在稀疏X射线投影等降质测量场景中的卓越性能。尽管大量深度学习方法受益于大规模监督数据集，能够将实验测量值直接映射为医学图像，但这些方法无法推广至未知的采集设置。相比之下，完全无监督技术（最值得注意的是基于分数的生成模型）近期在解决IIP时展现出与监督方法相当甚至更优的性能，同时在测试阶段对成像设置具有灵活性。然而，其应用受限于两个因素：（a）需要大量训练数据才能具备良好的泛化特性；（b）需要反向算子（如CT中的滤波反投影）将学习到的医学扫描先验分布与实验测量值进行条件约束。为克服这些问题，我们提出了一种针对生成潜在优化框架的无监督条件方法（cGLO），其中解码器网络的参数在无监督数据集上进行初始化。该解码器随后通过执行生成潜在优化用于重建，其损失函数直接比较来自建议重建的模拟测量值与实验测量值。所提出的方法在多种训练数据集规模下，通过稀疏视角CT进行测试，在大多数数据情况下展现出优于现有基于分数的策略的重建质量，并在训练数据集较小且投影角度减少时表现出更大的性能优势。此外，cGLO无需任何反向算子，甚至可将应用场景扩展至非线性IIP领域。