Diffusion models have been demonstrated as powerful deep learning tools for image generation in CT reconstruction and restoration. Recently, diffusion posterior sampling, where a score-based diffusion prior is combined with a likelihood model, has been used to produce high quality CT images given low-quality measurements. This technique is attractive since it permits a one-time, unsupervised training of a CT prior; which can then be incorporated with an arbitrary data model. However, current methods rely on a linear model of x-ray CT physics to reconstruct or restore images. While it is common to linearize the transmission tomography reconstruction problem, this is an approximation to the true and inherently nonlinear forward model. We propose a new method that solves the inverse problem of nonlinear CT image reconstruction via diffusion posterior sampling. We implement a traditional unconditional diffusion model by training a prior score function estimator, and apply Bayes rule to combine this prior with a measurement likelihood score function derived from the nonlinear physical model to arrive at a posterior score function that can be used to sample the reverse-time diffusion process. This plug-and-play method allows incorporation of a diffusion-based prior with generalized nonlinear CT image reconstruction into multiple CT system designs with different forward models, without the need for any additional training. We develop the algorithm that performs this reconstruction, including an ordered-subsets variant for accelerated processing and demonstrate the technique in both fully sampled low dose data and sparse-view geometries using a single unsupervised training of the prior.

翻译：扩散模型已被证明是CT重建与复原中强大的深度学习图像生成工具。近期，扩散后验采样技术将基于分数的扩散先验与似然模型相结合，能够在给定低质量测量数据的情况下生成高质量CT图像。该技术具有显著优势，因其允许对CT先验进行一次性无监督训练，随后可与任意数据模型结合。然而，现有方法依赖于X射线CT物理的线性模型进行图像重建或复原。尽管在透射断层扫描重建问题中常采用线性化近似，但这本质上是对真实非线性前向模型的近似。本文提出一种新方法，通过扩散后验采样解决非线性CT图像重建的逆问题。我们通过训练先验分数函数估计器实现传统无条件扩散模型，并应用贝叶斯规则将该先验与源自非线性物理模型的测量似然分数函数相结合，得到可用于逆向时间扩散过程采样的后验分数函数。这种即插即用方法可将基于扩散的先验与广义非线性CT图像重建结合，适配具有不同前向模型的多种CT系统设计，且无需任何额外训练。我们开发了实现该重建的算法，包括用于加速处理的有序子集变体，并在先验仅需一次无监督训练的条件下，分别针对全采样低剂量数据和稀疏视角几何结构验证了该技术的有效性。