Exact and Calibrated Diffusion Reconstruction for Digital Breast Tomosynthesis

Abstract

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 $\rho\to0$ 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.