量化多源成像剂量代价，发现先验可降噪但难通用

Objective. Temporal CT (TCT) fires three X-ray sources simultaneously onto a shared detector, creating a pre-reconstruction inverse problem: each bundle of five Poisson intensities sums unlabeled photon contributions from three line integrals. Because the measurement sums exponentials rather than forming one Beer-Lambert product, log and sum do not commute and the inversion is nonlinear. We quantify the dose cost this multiplexing imposes and how closely estimators can approach the resulting limit. Approach. We treat the 5x3 bundle as a model problem for multiplexed photon aggregation, with TCT the motivating instance. Closed-form Cramer-Rao bounds (CRBs) are expressed as dose-inflation factors against an equal-dose single-source floor, and two estimators, a structured classical per-bundle estimator (SNN1) and a physics-motivated residual network, are benchmarked on three datasets: i.i.d. synthetic, an analytical phantom, and single-patient bundles. Main results. Aggregation imposes a structural loss: at equal attenuation only 43% of single-source Fisher information survives for the endpoint paths and 23% for the middle path, fixing constant CRB inflation ratios sqrt(7/3) = 1.53 and sqrt(13/3) = 2.08. SNN1 reaches the endpoint CRBs within a few percent but degrades on the middle path under photon starvation. A learned joint prior closes much of this gap and, on single-patient data, pushes middle-path noise below the equal-dose floor: a Bayesian effect (interpolation within one anatomy) from the prior, not the architecture, and not a generalizable dose gain. A mismatched prior fails out-of-distribution. Significance. The structure (a Poisson sum of exponentials) and the methodology are not specific to TCT. Whether a learned prior yields a generalizable dose reduction is the open question a companion paper addresses through a multi-patient corpus.