Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview

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.

Evaluating Adversarial Robustness of Low dose CT Recovery

Low dose computed tomography (CT) acquisition using reduced radiation or sparse angle measurements is recommended to decrease the harmful effects of X-ray radiation. Recent works successfully apply deep networks to the problem of low dose CT recovery on bench-mark datasets. However, their robustness needs a thorough evaluation before use in clinical settings. In this work, we evaluate the robustness of different deep learning approaches and classical methods for CT recovery. We show that deep networks, including model-based networks encouraging data consistency, are more susceptible to untargeted attacks. Surprisingly, we observe that data consistency is not heavily affected even for these poor quality reconstructions, motivating the need for better regularization for the networks. We demonstrate the feasibility of universal attacks and study attack transferability across different methods. We analyze robustness to attacks causing localized changes in clinically relevant regions. Both classical approaches and deep networks are affected by such attacks leading to changes in the visual appearance of localized lesions, for extremely small perturbations. As the resulting reconstructions have high data consistency with the original measurements, these localized attacks can be used to explore the solution space of the CT recovery problem.