This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one-dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the subspace of data-consistent solutions through explicit guidance to satisfy specific semantic or textural properties.

翻译：本文综述了当前利用变分方法和机器学习解决成像逆问题的研究进展。特别关注点估计器及其对抗扰动的鲁棒性，在此背景下提供了一维示例问题的数值实验结果，展示了不同方法的鲁棒性并实证验证了理论保证。本综述的另一重点是通过显式引导满足特定语义或纹理特性，探索数据一致性解的子空间。