Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview
This is an incremental overview paper for researchers in imaging and inverse problems, summarizing existing approaches without introducing new methods.
The paper reviews variational and machine learning methods for solving inverse problems in imaging, focusing on robustness against adversarial perturbations and exploring data-consistent solutions with specific properties, with numerical experiments on a toy problem showing robustness and verifying theoretical guarantees.
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.