Robustness and Exploration of Variational and Machine Learning
  Approaches to Inverse Problems: An Overview
Alexander Auras Kanchana Vaishnavi Gandikota Hannah Droege Michael Moeller
This paper attempts to provide 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.