提出精确数据一致的扩散重建方法，解决乳腺摄影中的伪影与不确定性问题。
Exact and Calibrated Diffusion Reconstruction for Digital Breast Tomosynthesis
- 用欧几里得投影替代扩散采样中的近似更新，确保数据完全一致
- 数据残差降至2.4×10⁻¹³，且样本方差仅存在于未测量空间
- 首次实现有限角度乳腺断层成像的可校准不确定性估计，适合临床可信度评估
有限角度数字乳腺断层成像（DBT）从少量低剂量投影中重建三维图像，典型九视角、25°扫描协议下超过98%的图像空间未被测量，需依赖学习先验填补缺失楔形区域。现有条件扩散先验虽具良好视觉质量，但存在三个临床障碍：数据不一致、幻觉位置无定位、不确定性未校准。本文通过将条件扩散采样中每步的近端更新替换为精确的欧几里得投影，强制满足测量约束，该投影基于一次性的m维对偶系统与矩阵分解$AA^{ op}$，每步耗时仅4.5毫秒（提速248倍），使数据残差降至双精度极限（2.4×10⁻¹³）。理论证明其为近端步的ρ→0极限，给出无害定理，并表明精确一致样本集合的方差仅支持于null(A)。因此，均值误差完全位于未测量子空间，由不确定性图覆盖。在患者衍生乳腺体模上，该方法提升保真度且不损失深度分辨率。相反，在更新后应用近端步会降低质量，凸显一致性步骤位置的关键性。等距校准将集合发散调整至校准误差尺度（期望校准误差0.029→0.008；标准化误差4.7→0.96），优于纯先验。还修复了部署投影器中存在的20.3%伴随不匹配问题，通过记录显式算子实现。这是首个兼具数据一致性和不确定性校准的有限角度DBT学习重建方法。求解器自然退化至噪声情况下的偏差球和最大后验模式。
原文摘要 · Abstract (English)
Limited-angle digital breast tomosynthesis (DBT) reconstructs a volume from a few low-dose projections over a narrow arc. At a representative nine-view, $25^{\circ}$ protocol more than 98% of image space is unmeasured, so a learned prior must supply structure in the missing wedge. Conditional diffusion priors achieve strong perceptual quality here but leave three clinical obstacles: inexact data consistency, unlocalized hallucination, and uncalibrated uncertainty. We enforce measurements exactly by replacing the per-step proximal update of a conditional diffusion sampler with exact Euclidean projection onto the data-consistent set, computed via an $m$-dimensional dual system with a one-time Gram matrix $AA^{\top}$ factorization. This projection costs 4.5 ms per step (a $248\times$ speedup) and drives the data residual to the double-precision floor ($2.4\times10^{-13}$). We prove it is the $ρ\to0$ limit of the proximal step, provide a no-harm theorem, and show that exactly consistent sample ensembles have variance supported on null($A$). Thus, the mean's entire error lies in the unmeasured subspace covered by the uncertainty map. On patient-derived breast phantoms, this improves fidelity at no depth-resolution cost. Conversely, a proximal step applied post-update degrades quality, isolating the consistency step's placement as decisive. Isotonic recalibration brings the ensemble spread to a calibrated error scale (expected calibration error $0.029\to0.008$; standardized error $4.7\to0.96$), ranking errors better than the pure prior. We also repair a 20.3% adjoint mismatch in a deployed projector via a materialized operator of record. This is the first data-consistent, uncertainty-calibrated learned reconstruction for limited-angle DBT. The solver naturally relaxes to discrepancy-ball and maximum-a-posteriori modes for noisy measurements.
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