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

2026-02-03

AI Summary

This work addresses the challenges of reconstruction instability and uncertainty quantification in diffuse optical tomography (DOT), which arise from severe ill-posedness, noise, and modeling errors. The authors propose a hybrid fractional regularization method that integrates data-driven priors with physical models. Built upon a fractional diffusion model, the approach enables robust posterior sampling of absorption and scattering parameters within a Bayesian inverse problem framework. Notably, it provides the first experimental validation of the unconditional-on-conditional score (UCoS) representation on real DOT data. Experiments demonstrate that the proposed method significantly outperforms conventional model-driven approaches on both simulated and measured datasets, yielding posterior samples with lower variance and closer alignment to the true distribution—particularly under highly ill-posed conditions or in the presence of modeling inaccuracies.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• diffuse optical tomography
• ill-posed inverse problem
• uncertainty quantification
• modelling error
• Bayesian inverse problems

Innovation

• score-based diffusion models
• diffuse optical tomography
• uncertainty quantification
• mixed score regularization
• Bayesian inverse problems