Lunz Sebastian, Hauptmann Andreas, Tarvainen Tanja, Schönlieb Carola-Bibiane, Arridge Simon
University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Cambridge.
University of Oulu, Research Unit of Mathematical Sciences; University College London, Department of Computer Science, London.
SIAM J Imaging Sci. 2021 Jan;14(1):92-127. doi: 10.1137/20M1338460. Epub 2021 Jan 26.
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.
我们讨论了针对逆问题学习数据驱动的显式模型校正的可能性，以及这种模型校正是否可用于变分框架内以获得正则化重建。本文讨论了学习这种正向模型校正的概念性困难，并进而提出一种可能的解决方案，即作为在数据空间和求解空间中都进行显式校正的正向 - 伴随校正。然后，我们推导了在何种条件下，带有学习到的校正的变分问题的解会收敛到使用正确算子获得的解。所提出的方法在有限视角光声层析成像的应用中进行了评估，并与贝叶斯近似误差方法的既定框架进行了比较。
