Calibrated per-pixel uncertainty for low-dose paediatric chest-radiograph denoising at no fidelity cost

Background. Deep denoisers restore low-dose chest radiographs but emit a single point estimate with no indication of where the output is reliable, so a confident-looking reconstruction can be locally wrong. In paediatric radiography, where the radiation-dose imperative is sharpest, we ask whether a per-pixel uncertainty map can be attached at no meaningful cost to reconstruction quality. Methods. We develop PP-VAE-Hformer, a hybrid convolution-transformer denoiser with a variational-autoencoder bottleneck (epistemic uncertainty map) and a heteroscedastic dual head (aleatoric map), and run a 19-arm ablation isolating five composite-loss terms on Poisson-Gaussian-degraded paediatric chest radiographs (Kermany collection; 624-image held-out test set), against eight discriminative baselines retrained on identical data and noise. Calibration is assessed by reliability diagrams and post-hoc-scaling; comparisons use Bonferroni-corrected Welch tests with Cohens d as the primary discriminant. Results. A heteroscedastic negative-log-likelihood (NLL) objective buys a calibrated aleatoric map for 1.2 dB PSNR, which two-stage fine-tuning recovers to a statistically indistinguishable 0.010 dB. For the variational variant the Kullback-Leibler (KL) annealing schedule, not the bottleneck itself, is decisive: cyclic annealing closes a 1.10 dB gap over posterior-collapsing linear warmup. Predicted uncertainty tracks realised error (Pearson r > 0.8) with an optimal recalibration scale within 1% of unity. A matched-severity cross-degradation test shows this calibration is model-circular, however: at equal severity the aleatoric map becomes modestly (8-16%, a lower bound) over-confident once the noise model changes, and the Monte-Carlo epistemic map is a weaker error predictor that does not compensate. We additionally document a previously unreported destructive interaction between structural-similarity and Sobel-edge supervision at literature-default weights. Conclusions. A calibrated per-pixel uncertainty map can be attached to a paediatric low-dose CXR denoiser at effectively no reconstruction cost. Its near-perfect calibration is tied to the trained (inverse-crime) noise model, and the Monte-Carlo epistemic map does not reliably substitute where the aleatoric map fails, so an architecture-independent uncertainty estimate (e.g. deep ensembling), a blinded reader study, and real low-dose data are the immediate next steps. Keywords. image denoising; uncertainty quantification; calibration; variational autoen-coder; paediatric chest radiography; low-dose imaging