标题： 基于不完整数据的投影嵌入扩散桥用于CT重建 显示英文标题

标题： Projection Embedded Diffusion Bridge for CT Reconstruction from Incomplete Data

摘要： 从不完整的投影数据中重建CT图像仍然具有挑战性，这是由于问题的不适定性质。扩散桥模型最近在从相应的滤波反投影（FBP）重建中恢复干净图像方面显示出前景，但将数据一致性纳入这些模型的研究仍 largely 未被探索。将数据一致性纳入可以提高重建保真度，通过将重建图像与观察到的投影数据对齐，并可以通过整合投影中的结构信息来增强细节恢复。在本工作中，我们提出了投影嵌入扩散桥（PEDB）。PEDB引入了一种新颖的反向随机微分方程（SDE），以从干净图像的分布中进行采样，该分布同时基于FBP重建和不完整的投影数据。通过在采样干净图像时明确地基于投影数据，PEDB自然地融入了数据一致性。我们将投影数据嵌入到反向SDE的得分函数中。在某些假设下，我们推导出后验得分的可处理表达式。此外，我们引入了一个自由参数来控制反向过程中的随机性水平。我们还为反向SDE设计了一个离散化方案，以减轻离散化误差。大量实验表明，PEDB在从三种类型的不完整数据（包括稀疏视角、有限角度和截断投影）进行CT重建中表现出色。对于每种类型，PEDB在标准、噪声和领域转移评估中都优于评估的最先进扩散桥模型。 显示英文摘要

摘要： Reconstructing CT images from incomplete projection data remains challenging due to the ill-posed nature of the problem. Diffusion bridge models have recently shown promise in restoring clean images from their corresponding Filtered Back Projection (FBP) reconstructions, but incorporating data consistency into these models remains largely underexplored. Incorporating data consistency can improve reconstruction fidelity by aligning the reconstructed image with the observed projection data, and can enhance detail recovery by integrating structural information contained in the projections. In this work, we propose the Projection Embedded Diffusion Bridge (PEDB). PEDB introduces a novel reverse stochastic differential equation (SDE) to sample from the distribution of clean images conditioned on both the FBP reconstruction and the incomplete projection data. By explicitly conditioning on the projection data in sampling the clean images, PEDB naturally incorporates data consistency. We embed the projection data into the score function of the reverse SDE. Under certain assumptions, we derive a tractable expression for the posterior score. In addition, we introduce a free parameter to control the level of stochasticity in the reverse process. We also design a discretization scheme for the reverse SDE to mitigate discretization error. Extensive experiments demonstrate that PEDB achieves strong performance in CT reconstruction from three types of incomplete data, including sparse-view, limited-angle, and truncated projections. For each of these types, PEDB outperforms evaluated state-of-the-art diffusion bridge models across standard, noisy, and domain-shift evaluations.