Sampling-free Monte Carlo dropout approximation for single-pass uncertainty quantification in deep learning-based PET reconstructions

Abstract Objective: Medical image reconstructions using deep learning (DL) can rapidly generate high-quality images from degraded measurements, but their clinical adoption remains challenging, largely due to the lack of fast and reliable methods to quantify aleatoric (data-driven) and epistemic (model-driven) uncertainties on a per-prediction basis. We aim to develop a computationally efficient approach for estimating both uncertainties at the voxel level in DL-based image reconstruction within a single inference run. Approach: We present a moment propagation-based framework that analytically approximates the conventional, multi-realization Monte Carlo (MC) dropout by propagating feature-map means and marginal variances through network layers, followed by a pre-calibrated correction table to compensate for covariance effects omitted in the approximation. This enables joint estimation of reconstruction, aleatoric uncertainty and epistemic uncertainty in a single forward pass. The proposed framework was implemented on top of FastPET -- a network model synthesizing PET reconstructions from time-of-flight histo-images -- and evaluated in a patient pilot study of 26 total-body PET/CT acquisitions (16 [18F]-FDG and 10 [18F]-PSMA cases). Main Results: Proposed method achieved relatively strong agreement with the 50-pass MC approach, with absolute differences <0.5% for reconstruction, <4.2% for aleatoric uncertainty and <9.8% for epistemic uncertainty, along with narrow spreads across patients and tracer types, while reducing computation time by ~40-fold. In a complementary proof-of-concept low-count experiment, regional tracer uptake confidence intervals (CIs, derived from propagated uncertainties) widened with increased noise level, and reference uptakes consistently fell close to CI boundaries, indicating the proposed method could provide roughly calibrated uncertainty magnitudes reflecting quantitative prediction errors. Significance: The proposed approach provides a sampling-free and relatively accurate approximation to the multi-pass MC-based uncertainty estimation in the histo-image-based DL PET reconstruction framework. Per-prediction uncertainty quantification enables direct assessment of AI confidence and potentially supports more reliable and informed decision-making.