[Paper Review] Principled Confidence Estimation for Deep Computed Tomography

Matteo Gätzner, Johannes Kirschner|arXiv (Cornell University)|Feb 5, 2026

Medical Imaging Techniques and Applications0 citations

TL;DR

This paper introduces a principled framework to construct anytime, finite-sample confidence regions with coverage guarantees for CT reconstructions, integrating deep learning priors (U-Nets, ensembles, diffusion) with sequential likelihood mixing to quantify uncertainty and detect hallucinations.

ABSTRACT

We present a principled framework for confidence estimation in computed tomography (CT) reconstruction. Based on the sequential likelihood mixing framework (Kirschner et al., 2025), we establish confidence regions with theoretical coverage guarantees for deep-learning-based CT reconstructions. We consider a realistic forward model following the Beer-Lambert law, i.e., a log-linear forward model with Poisson noise, closely reflecting clinical and scientific imaging conditions. The framework is general and applies to both classical algorithms and deep learning reconstruction methods, including U-Nets, U-Net ensembles, and generative Diffusion models. Empirically, we demonstrate that deep reconstruction methods yield substantially tighter confidence regions than classical reconstructions, without sacrificing theoretical coverage guarantees. Our approach allows the detection of hallucinations in reconstructed images and provides interpretable visualizations of confidence regions. This establishes deep models not only as powerful estimators, but also as reliable tools for uncertainty-aware medical imaging.

Motivation & Objective

• Develop confidence sequences with finite-time, anytime validity for CT reconstruction under Poisson noise and Beer-Lambert forward model.
• Enable uncertainty quantification that tightens with better reconstructions and supports hallucination detection.
• Demonstrate integration of deep learning priors (U-Nets, ensembles, diffusion models) into principled uncertainty estimation for CT.
• Provide interpretable pixel-wise uncertainty visualizations and practical diagnostics for safety-critical imaging.

Proposed method

• Model the CT forward process with Beer-Lambert law and Poisson noise in a parallel-beam geometry.
• Construct confidence sequences C_t as level sets of the negative log-likelihood with a time-dependent threshold beta_t.
• Define beta_t via sequential likelihood mixing using a sequence of mixing distributions mu_s that depend only on data up to time s.
• Allow mixing distributions to be point predictions or mixtures from generative models (e.g., U-Net ensembles, diffusion models).
• Prove that the resulting C_t is a (1-delta)-confidence sequence for the ground-truth x* with finite-time coverage.
• Demonstrate how to project high-dimensional C_t into pixel-wise uncertainty visualizations and use them for hallucination detection.

Experimental results

Research questions

• RQ1 Can principled sequential confidence sequences provide finite-sample, anytime-valid uncertainty regions for CT reconstructions under realistic forward models?
• RQ2 How do deep learning priors (single predictions, ensembles, diffusion models) affect the tightness and validity of the confidence regions?
• RQ3 Can the framework detect model hallucinations and reveal pixel-wise uncertainty interpretable by clinicians or operators?
• RQ4 How do the confidence regions and visualizations perform across medical, industrial, and materials-science CT datasets?
• RQ5 What are practical strategies to project high-dimensional confidence sets into informative, pixel-wise uncertainty maps?

Key findings

• Deep learning priors yield substantially tighter confidence regions than classical baselines like FBP or MLE under the same coverage guarantees.
• Mixture-based mixing (e.g., U-Net ensembles, diffusion models) consistently lowers the sequential negative log-likelihood threshold beta_t compared to mean-prediction approaches, yielding tighter C_t.
• The method achieves statistical coverage (<= 0.05 empirical crossover rate) across datasets and intensities, with diffusion-based mixing providing particularly tight bounds.
• Confidence sequences enable effective detection of geometric misalignment and model hallucinations by flagging reconstructions inconsistent with measurement data.
• Pixel-wise uncertainty maps can be derived from C_t via worst-case optimization or diffusion-bound sampling, enabling interpretable visualization of uncertainty.
• The framework generalizes to both classical and deep-learning reconstructions and works with the non-linear forward model and Poisson noise used in CT.