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This research applies score-based diffusion models to the challenging inverse problem of diffuse optical tomography, specifically addressing severe ill-posedness caused by noise and limited-view geometries. By introducing a mixed regularization strategy that combines learned priors with model-based components, the study demonstrates superior reconstruction accuracy over classical methods and standard diffusion approaches in experimental settings. The work provides theoretical justification for using mixture distributions to stabilize posterior sampling in high-noise biological imaging scenarios.
Score-based diffusion models for severely ill-posed problems in diffuse optical tomography
arXiv:2602.03449v2 Announce Type: replace-cross Abstract: Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems, enabling high-quality reconstructions in inverse problems by leveraging expressive prior distributions learned from empirical data. Despite their strong empirical performance and growing interest within the machine learning community, their behaviour in realistic, severely ill-posed inverse problems with experimental measurement data remains under-explored. Diffuse optical tomography (DOT) is an inverse boundary value problem that uses boundary measurements of near-infrared light to recover spatially varying absorption and scattering parameters in biological tissue. The problem is highly ill-posed and particularly sensitive to both measurement noise and modelling errors. We introduce a regularization strategy by constructing a mixed score consisting of a learned component and a model-based component. We show that the resulting mixed score approximates the score of a corresponding mixture distribution locally and in the small diffusion-time regime, providing a theoretical justification for the approach. We compare four approaches for difference imaging in DOT: a classical model-based method, an approximate score-based diffusion method (DPS), an exact posterior sampling method (UCoS) and a novel, regularized version of UCoS. We show that both the model-based approach and approximate diffusion-based sampling degrade significantly in the presence of limited-view geometry and real experimental data, whereas UCoS yields more accurate reconstructions.
Abstract:Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems, enabling high-quality reconstructions in inverse problems by leveraging expressive prior distributions learned from empirical data. Despite their strong empirical performance and growing interest within the machine learning community, their behaviour in realistic, severely ill-posed inverse problems with experimental measurement data remains under-explored. Diffuse optical tomography (DOT) is an inverse boundary value problem that uses boundary measurements of near-infrared light to recover spatially varying absorption and scattering parameters in biological tissue. The problem is highly ill-posed and particularly sensitive to both measurement noise and modelling errors. We introduce a regularization strategy by constructing a mixed score consisting of a learned component and a model-based component. We show that the resulting mixed score approximates the score of a corresponding mixture distribution locally and in the small diffusion-time regime, providing a theoretical justification for the approach. We compare four approaches for difference imaging in DOT: a classical model-based method, an approximate score-based diffusion method (DPS), an exact posterior sampling method (UCoS) and a novel, regularized version of UCoS. We show that both the model-based approach and approximate diffusion-based sampling degrade significantly in the presence of limited-view geometry and real experimental data, whereas UCoS yields more accurate reconstructions.
Machine Learning (stat.ML); Machine Learning (cs.LG); Applications (stat.AP)
arXiv:2602.03449 [stat.ML]
(or arXiv:2602.03449v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2602.03449 Focus to learn more arXiv-issued DOI via DataCite
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