Exact and Calibrated Diffusion Reconstruction for Digital Breast Tomosynthesis

Limited-angle digital breast tomosynthesis (DBT) reconstructs a volume from a few low-dose projections over a narrow arc. At a representative nine-view, 25circ 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 AAtop factorization. This projection costs 4.5 ms per step (a 248× speedup) and drives the data residual to the double-precision floor (2.4×10-13). We prove it is the ρ→0 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→0.008; standardized error 4.7→0.96), 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.