发表机构
Imade Bouftini（Imade Bouftini）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对有限角度数字乳腺断层合成，提出用精确欧几里得投影替换近端更新来确保数据一致性，通过等渗重新校准解决不确定性问题，修复投影仪伴随不匹配，实现首个数据一致、不确定性校准的学习重建，提高了重建保真度。
AI 中文摘要
有限角度数字乳腺断层合成（DBT）通过少量低剂量投影在窄弧上重建体积。在典型的九视图、25°协议中，超过98%的图像空间未被测量，因此学习先验必须在缺失楔中提供结构。条件扩散先验在此处实现了较强的感知质量，但存在三个临床障碍：数据一致性不准确、幻觉未定位和不确定性未校准。我们通过用精确的欧几里得投影替换条件扩散采样器的每步近端更新来精确执行测量，通过具有一次性Gram矩阵 \(AA^{\top}\) 分解的 \(m\) 维对偶系统计算到数据一致集上。该投影每步成本为4.5毫秒（加速248倍）并将数据残差驱动到双精度下限（\(2.4\times10^{-13}\)）。我们证明它是近端步的 \(\rho\to0\) 极限，提供无危害定理，并表明精确一致的样本集合的方差支持在 \(null(A)\) 上。因此，均值的整个误差位于不确定性映射覆盖的未测量子空间中。在患者衍生的乳腺模型上，这在不损失深度分辨率的情况下提高了保真度。相反，更新后应用近端步会降低质量，将一致性步的位置隔离为决定性因素。等渗重新校准将集合扩展带到校准误差尺度（预期校准误差从0.029降至0.008；标准化误差从4.7降至0.96），比纯先验更好地对误差进行排序。我们还通过记录的物化算子修复了已部署投影仪中20.3%的伴随不匹配。这是有限角度DBT的第一个数据一致、不确定性校准的学习重建。求解器自然地放松到用于噪声测量的差异球和最大后验模式。
英文摘要
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.
CommentsarXiv admin comment: This version has been removed by arXiv administrators as the submitter did not have the rights to agree to the license at the time of submission
