Variational Bayes uncertainty quantification for inverse problems

逆问题的变分贝叶斯不确定性量化

• 批准号: 2597238
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2597238
• 关键词: Variational; Bayes; uncertainty; quantification; inverse

Many popular regularised estimators in linear inverse problems arising from PET and other tomographic medical imaging techniques can be interpreted as maximum a posteriori (MAP) estimators. An analysis of the full Bayesian posterior in these problems has been proposed as a procedure for uncertainty quantification, for which there is a significant need in medical applications. However, algorithms for posterior sampling can be expensive and difficult to tune. The purpose of the project is to develop variational Bayes posterior approximations of the posterior, and prove guarantees on the convergence of algorithms and on the quality of the approximation.

PET和其他断层医学成像技术中的线性逆问题中的许多流行的正则化估计可以被解释为最大后验（MAP）估计。在这些问题中的完整贝叶斯后验分析已被提出作为不确定性量化的程序，在医学应用中有很大的需求。然而，用于后验采样的算法可能是昂贵的并且难以调整。该项目的目的是开发后验的变分贝叶斯后验近似，并证明算法收敛性和近似质量的保证。