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）的典型实例，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。尽管大多数深度学习方法依赖大规模监督数据集直接实现实验测量数据到医学影像的映射，但这些方法无法泛化到未知采集场景。相比之下，全无监督技术（尤其是基于分数的生成模型）近期在解决IIP问题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场景具有灵活适应性。然而，其应用受限于两个因素：（a）需要大量训练数据才能获得良好的泛化特性；（b）需要如CT中滤波反投影这样的反向算子，以将医学影像的预训练先验分布与实验测量数据相关联。为克服这些问题，我们提出了一种面向生成式潜在优化框架的无监督条件化方法（cGLO），其中解码器网络的参数在无监督数据集上初始化。该解码器随后通过执行生成式潜在优化用于重建，优化过程的损失函数直接比较从候选重建结果模拟的测量数据与实验测量数据。经多组训练数据集规模下的稀疏视角CT实验验证，该方法在大多数数据场景下展现出优于当前最先进的基于分数策略的重建质量，且在训练数据集较小、投影角度减少时性能优势更为显著。此外，cGLO无需任何反向算子，有望将应用场景扩展至非线性IIP领域。