论文标题
在学习逆问题中学习的操作员校正
On Learned Operator Correction in Inverse Problems
论文作者
论文摘要
我们讨论了学习数据驱动的显式模型校正的可能性，以及是否可以在变异框架中使用此类模型校正来获得正则重建。本文讨论了学习这样的远期模型校正的概念困难，并继续提出可能的解决方案，例如在数据和解决方案空间中明确纠正的前进校正校正。然后，我们得出条件，在哪些条件下，对变异问题的解决方案则通过学习的校正收敛到使用正确操作员获得的解决方案。在有限查看光声断层扫描的应用程序上评估了所提出的方法，并将其与贝叶斯近似误差法的既定框架进行了比较。
We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the conceptual difficulty to learn such a forward model correction and proceeds to present a possible solution as forward-adjoint correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of Bayesian approximation error method.
