SIAM Journal on Imaging Sciences, Volume 14, Issue 1, Page 92-127, January 2021.
We discuss the possibility of learning a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularized reconstructions. This paper discusses the conceptual difficulty of learning such a forward model correction and proceeds to present a possible solution as a 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 the Bayesian approximation error method.

中文翻译：

---

反问题中的习得算子校正

SIAM影像科学杂志，第14卷，第1期，第92-127页，2021年1月。
我们讨论了学习针对逆问题的数据驱动的显式模型校正的可能性，以及是否可以在变分框架内使用这种模型校正来获得正则化重构。本文讨论了学习这种前向模型校正的概念难度，并提出了一种可能的解决方案，作为可在数据和解决方案空间中进行显式校正的前向伴随校正。然后，我们得出条件，在该条件下，具有学习到的校正的变分问题的解收敛到由正确的算子获得的解。在有限视图光声层析成像的应用中评估了所提出的方法，并将其与贝叶斯近似误差方法的已建立框架进行了比较。