基于分数的扩散模型用于扩散光学断层扫描与不确定性量化
Score-based diffusion models for severely ill-posed problems in diffuse optical tomography
AI总结：
本文提出基于分数的扩散模型用于扩散光学断层扫描，通过混合分数正则化方法提升病态问题的后验抽样性能。
摘要：
基于分数的扩散模型是一种最近开发的框架，用于贝叶斯反问题的后验抽样，在严重病态问题中通过利用从经验数据学习到的强大先验分布实现了最先进的性能。尽管在机器学习社区中引起了广泛关注，但对现实中的反问题在存在建模误差和利用物理测量数据方面的深入研究仍显不足。在本工作中，对条件分数函数的无条件表示框架（UCoS）在扩散光学断层扫描（DOT）中的线性化差分成像进行了评估。DOT利用近红外光的边界测量来估计生物组织中吸收和散射参数的空间分布。该问题高度病态，因此对噪声和建模误差非常敏感。我们引入了一种新的正则化方法，通过构造由学习和模型基成分组成的混合分数，以防止分数函数的过拟合。该方法的验证使用了模拟和实验测量数据。实验表明，数据驱动的先验分布在高度病态问题和存在建模误差的情况下，能够产生方差较低的后验样本，且围绕真实值中心，优于传统模型基估计。
英文摘要：
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.
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