Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements

TL;DR

The paper tackles objective, ground-truth-free evaluation of Bayesian imaging models by introducing a data fission–driven Bayesian cross-validation framework suitable for modern data-driven priors and diffusion/plug-and-play samplers. It defines two scoring rules—likelihood-based and perceptual, posterior-based—together with Monte Carlo approximations to quantify model fit and prior misspecification from a single noisy measurement. The method enables unsupervised model selection and misspecification diagnosis, including robust out-of-distribution detection in tasks like image deblurring and MRI reconstruction, with favorable accuracy and computational efficiency. This approach provides a practical, model-agnostic tool for reliable inference in imaging pipelines that rely on powerful learned priors, addressing a critical reliability gap in scientific and medical imaging applications.

Abstract

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.

Figures (20)

• Figure 1: Log difference between $p(y^+|y^-, \sigma_x^2)$ and $p(y^+|y^-, \sigma_x'^2)$ as a function of $\sigma_x'$ and for different $\alpha$, averaged over the injected noise $\mathbf{w}$. The true prior standard deviation is $\sigma_x=1$.
• Figure 2: Log difference between $p(y^+|y^-, \sigma_x^2)$ and $p(y^+|y^-, \sigma_x'^2)$ as a function of $\sigma_x'$ and for different numbers of noise realizations $K$, with $\alpha = 0.5$. The true prior standard deviation is $\sigma_x=1$.
• Figure 3: Examples of blurred measurements, generated by using the blur kernel $\kappa_{\mathcal{G}}(2)$.
• Figure 4: Profile of the considered blur kernels, their similarity makes model selection difficult.
• Figure 5: Posterior samples from $p(x|y^-)$ for $\alpha=0.1$, $\sigma_\kappa=0.5$, for some test natural image examples.