Principled Confidence Estimation for Deep Computed Tomography

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.

💡 Research Summary

The paper introduces a rigorous uncertainty quantification framework for X‑ray computed tomography (CT) reconstruction that delivers finite‑sample, anytime‑valid confidence regions with provable coverage guarantees. Building on the sequential likelihood mixing (SLM) methodology (Kirschner et al., 2025), the authors model the CT forward problem using the Beer‑Lambert law with Poisson noise, yielding a log‑linear likelihood for each projection angle. For a candidate image (x), the negative log‑likelihood after (t) measurements is (L_t(x)= -\sum_{s=1}^t \log p_x(y_s\mid\alpha_s,I_0)). The confidence set at time (t) is defined as the level set (C_t={x: L_t(x)\le \beta_t+\log(1/\delta)}), where (\beta_t) is a data‑driven threshold.

Crucially, (\beta_t) is chosen as the cumulative negative log‑likelihood of the observed data under a sequence of predictions (\hat x_{s-1}) that are constructed only from measurements up to step (s-1). Formally, \