Score-based diffusion models for diffuse optical tomography with uncertainty quantification

TL;DR

This paper evaluates score-based diffusion models for diffuse optical tomography, demonstrating that a hybrid learned and model-based prior improves uncertainty quantification and robustness against noise and modeling errors.

Contribution

It introduces a novel regularization method for score-based models in DOT, combining learned and physical model components to enhance posterior sampling.

Findings

Data-driven prior yields low-variance posterior samples.

Method remains effective despite high ill-posedness and modeling errors.

Experimental validation confirms improved accuracy over classical methods.

Abstract

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from empirical data. Despite generating significant interest especially in the machine-learning community, a thorough study of realistic inverse problems in the presence of modelling error and utilization of physical measurement data is still outstanding. In this work, the framework of unconditional representation for the conditional score function (UCoS) is evaluated for linearized difference imaging in diffuse optical tomography (DOT). DOT uses boundary measurements of near-infrared light to estimate the spatial distribution of absorption and scattering parameters in biological tissues. The problem is highly ill-posed and thus sensitive to noise and modelling errors. We introduce a novel regularization approach that prevents overfitting of the score function by constructing a mixed score composed of a learned and a model-based component. Validation of this approach is done using both simulated and experimental measurement data. The experiments demonstrate that a data-driven prior distribution results in posterior samples with low variance, compared to classical model-based estimation, and centred around the ground truth, even in the context of a highly ill-posed problem and in the presence of modelling errors.