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

TL;DR

This paper introduces a new unsupervised Bayesian model selection and misspecification detection method for imaging inverse problems, effective with noisy, partial measurements and compatible with modern machine learning priors.

Contribution

It proposes a novel combination of Bayesian cross-validation and data fission for efficient model evaluation in imaging, applicable to any Bayesian sampler.

Findings

Achieves high accuracy in model selection and misspecification detection.

Operates with low computational cost.

Compatible with various Bayesian imaging samplers.

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.