Robustness and exploration of variational and machine learning approaches to inverse problems: An overview

@article{https://doi.org/10.1002/gamm.202470003, author = {Auras, Alexander and Gandikota, Kanchana Vaishnavi and Droege, Hannah and Moeller, Michael}, title = {Robustness and exploration of variational and machine learning approaches to inverse problems: An overview}, journal = {GAMM-Mitteilungen}, volume = {n/a}, number = {n/a}, pages = {e202470003}, keywords = {explorability, inverse problems, machine learning, robustness}, doi = {https://doi.org/10.1002/gamm.202470003}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/gamm.202470003}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/gamm.202470003}, abstract = {Abstract 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.} }