发表机构
University of Cambridge（剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对稀疏视图和有限角度CT，提出几何感知扩散引导随机重建框架，利用噪声加权拉回度量自适应调整更新与探索，实现高质量重建与不确定性估计。
AI 中文摘要
稀疏视图计算机断层扫描（CT）可减少辐射剂量和采集时间，并可能减轻运动伪影。然而，角度欠采样提供的信息不足以唯一且稳定地确定图像。有限角度CT源于角度覆盖受限，产生与缺失角度范围相关的强方向性信息损失。在这两种情况下，图像方向可能被强烈观测、弱约束或不可观测，导致严重的病态性和重建模糊性。现有的基于扩散的方法通过似然引导、数据一致性操作或范围-零空间校正来整合测量信息。然而，它们通常不利用采集过程中连续变化的测量灵敏度来共同塑造重建更新和随机探索。我们提出了一种用于稀疏视图和有限角度CT的几何感知扩散引导随机重建框架。其核心组件是由CT前向算子和测量噪声协方差构建的正则化噪声加权拉回度量。该度量根据方向测量灵敏度连续调整测量感知更新和随机探索，抑制沿强约束方向的变化，同时允许沿弱约束和不可观测方向进行更大探索。我们用正则化数据一致性校正和近似零空间受限随机扰动补充这种几何感知更新，使用前向和反向投影操作以及共轭梯度求解以无矩阵方式实现。在稀疏视图、噪声和有限角度CT上的实验展示了有竞争力的重建质量、强测量一致性和空间分辨的经验不确定性估计。
英文摘要
Sparse-view computed tomography (CT) reduces radiation dose and acquisition time and may mitigate motion artifacts. However, angular undersampling provides insufficient information to determine the image uniquely and stably. Limited-angle CT, arising from restricted angular coverage, produces strongly directional information loss associated with the missing angular range. In both settings, image directions may be strongly observed, weakly constrained, or unobservable, leading to severe ill-posedness and reconstruction ambiguity. Existing diffusion-based approaches incorporate measurement information through likelihood guidance, data-consistency operations, or range-null-space corrections. However, they do not generally use the continuously varying measurement sensitivity of the acquisition to jointly shape both reconstruction updates and stochastic exploration. We propose a geometry-aware diffusion-guided stochastic reconstruction framework for sparse-view and limited-angle CT. Its central component is a regularized noise-weighted pullback metric constructed from the CT forward operator and measurement-noise covariance. This metric continuously adapts both the measurement-aware update and stochastic exploration according to directional measurement sensitivity, suppressing changes along strongly constrained directions while permitting greater exploration along weakly constrained and unobservable directions. We complement this geometry-aware update with a regularized data-consistency correction and approximately null-space-restricted stochastic perturbations, implemented matrix-free using forward and backprojection operations together with conjugate-gradient solves. Experiments on sparse-view, noisy, and limited-angle CT demonstrate competitive reconstruction quality, strong measurement consistency, and spatially resolved empirical uncertainty estimates.
