PEEL: Physics-Enabled Evidential Learning for Identifiable Uncertainty in CT Imaging

Ge Wang

cs.AIAug 27, 2026

PEEL: Physics-Enabled Evidential Learning for Identifiable Uncertainty in CT Imaging

Authors: Ge Wang

Organizations: Rensselaer Polytechnic Institute · Biomedical Imaging Center, Rensselaer Polytechnic Institute, Troy, New York, USA

Abstract

Normal-inverse-gamma (NIG) regression is not uniquely identifiable from its marginal Student-t likelihood: the likelihood determines three combinations of four NIG parameters and is constant along a one-dimensional fiber. We identify that fiber using independent physical measurement. As an initial embodiment, a reconstruction network receives one noisy filtered-backprojection (FBP) image and is first trained only by Student-t negative log-likelihood to estimate the three identifiable coordinates (gamma, alpha, c). The network is then frozen; repeated physical-noise realizations propagated through its reconstruction output form a Monte Carlo (MC) teacher label for output-domain aleatoric variance. An aleatoric head attached to frozen features learns this label, after which (beta, nu) are recovered algebraically. On 30 held-out simulated objects at five photon levels, one-image predictions achieved pooled Spearman correlations of 0.832-0.951 against independent 400-repeat references, median within-image correlations were 0.834-0.947, and 98.81-99.55% of evaluated pixels satisfied the algebraic admissibility condition. The method needs no KL term, reference prior, evidence regularizer, or cross-loss weight.

Figures & tables

Figure 1: PEEL workflow with a sequential teacher–student design. Stage 1 trains $F_{\theta}$ from noisy FBP using only Student- $t$ NLL. Repeated physical-noise inputs propagated through frozen $F_{\theta^{\star}}$ generate $u_{\mathrm{ale}}^{\mathrm{MC}}$ . Stage 2 attaches $A_{\psi}$ to frozen features $h_{\theta^{\star}}$ and updates only $\psi$ .

Figure 2: Two-network architectures for PEEL. (a) In Stage 1, the reconstruction network $F_{\theta}$ maps a single noisy FBP realization to shared features $h_{\theta}$ and the identifiable Student- $t$ coordinates $(\hat{\gamma},\hat{\alpha},\hat{c})$ . (b) In Stage 2, with $F_{\theta}$ frozen, the aleatoric head $A_{\psi}$ uses $h_{\theta}$ from a single noisy realization to predict the output-domain aleatoric variance $\hat{u}_{\mathrm{ale}}$ , supervised by the Monte Carlo teacher $u_{\mathrm{ale}}^{\mathrm{MC}}$ constructed from repeated physical-noise realizations. The decoupled design avoids cross-loss coupling between reconstruction and aleatoric regression.

$I_{0}$	log-RMSE	Pooled $\rho$	Within-image $\rho$	Case-mean $\rho$	Admissible (%)
$1.50\times 10^{4}$	0.953	0.832	0.834	0.879	98.81
$2.25\times 10^{4}$	0.631	0.884	0.883	0.819	99.17
$3.50\times 10^{4}$	0.439	0.932	0.925	0.886	99.55
$5.25\times 10^{4}$	0.532	0.944	0.940	0.876	99.49
$8.00\times 10^{4}$	0.732	0.951	0.947	0.850	99.49

Table 1: One-image

u_{\mathrm{ale}}

prediction against independent

R_{\mathrm{ref}}=400

MC references on 30 held-out objects. All correlations are Spearman coefficients.

Figure 3: Representative held-out object at $I_{0}=5.25\times 10^{4}$ . Left: the single noisy FBP supplied at inference. Middle: output-domain $u_{\mathrm{ale}}^{\mathrm{ref}}$ from 400 independent physical-noise realizations. Right: $\widehat{u}_{\mathrm{ale}}$ predicted from the single FBP. The variance maps share identical color limits.

Explore similar work

PEEL-DDPM: Physics-Enabled Evidential Learning for the Denoising Diffusion Probabilistic Model
Sep 23, 2026Ge WangUncertainty Quantification Image Reconstruction
Biomedical Imaging Center, Rensselaer Polytechnic Institute Troy, New York, USA
ELECTRIC: Evidential Learning-Enhanced CT Reconstruction via Iterative Correction
Jul 27, 2026Ge WangEvidential Deep Learning Bayesian Inverse Problems
Department of Biomedical Engineering Department of Electrical, Computer and Systems Engineering Department of Computer Science Rensselaer Polytechnic Institute, Troy, New York, USA
PhyDiCT: Plug-and-Play CT Reconstruction from Sparse X-Rays via Differentiable Rendering and Strong Priors
Oct 7, 2026Weicheng Dai, Shantanu Ghosh, Kayhan BatmanghelichSparse-View CT Reconstruction 3D Medical Imaging
Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA

Sep 23, 2026J/K move · Enter open · S save

PEEL-DDPM: Physics-Enabled Evidential Learning for the Denoising Diffusion Probabilistic Model

Ge Wang

Biomedical Imaging Center, Rensselaer Polytechnic Institute Troy, New York, USA

Uncertainty Quantification Image Reconstruction Uncertainty Decomposition Diffusion-Based Inverse Problems Evidential Deep Learning Physics-Informed Diffusion Models

Open paper AskPDF arXiv

Normal-inverse-gamma (NIG) regression is not identifiable from its marginal Student-t likelihood: three combinations of four NIG parameters are determined, leaving one degree of freedom. We introduce PEEL-DDPM, a physics-enabled evidential learning framework for denoising diffusion probabilistic models. A measurement-conditioned DDPM is first trained with epsilon-MSE and then frozen. Its complete reverse trajectory produces a reconstruction, whose residual from the known training object is modeled by a final-image evidential network. The network learns only the identifiable Student-t coordinates, while repeated scanner-noise realizations and repeated diffusion trajectories provide a nested Monte Carlo estimate of final-image aleatoric variance, separated into scanner-induced and sampler-induced components. This measured variance resolves the remaining NIG ambiguity and yields a decomposition of predictive uncertainty into measurement, diffusion, and epistemic terms. The method uses sequential training without a cross-loss weighting coefficient. In a feasibility study on eight held-out objects, empirical central-interval coverages were 49.3%, 80.3%, 90.1%, and 95.6% for nominal 50%, 80%, 90%, and 95% intervals. The mean squared residual was 0.967 times the mean predicted variance, and a single-image aleatoric head achieved pooled Spearman correlation 0.785 against an independent nested reference. Across five dose levels, scanner-induced variance showed a log-log dose slope of -1.15, whereas sampler-induced variance remained nearly dose independent with slope -0.01. These results support PEEL-DDPM as a practical route to identifiable and physically interpretable uncertainty quantification in diffusion-based image reconstruction.

Abstract

Explore similar work

PEEL-DDPM: Physics-Enabled Evidential Learning for the Denoising Diffusion Probabilistic Model

ELECTRIC: Evidential Learning-Enhanced CT Reconstruction via Iterative Correction

PhyDiCT: Plug-and-Play CT Reconstruction from Sparse X-Rays via Differentiable Rendering and Strong Priors