Abstract

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. For example, recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks. In analogy to adversarial attacks in classification, it was shown that slight distortions in the input domain may cause severe artifacts. In this talk, we will shed new light on this concern and deal with a quantitative robustness analysis of deep-learning-based algorithms for solving underdetermined inverse problems. This covers compressed sensing with Gaussian measurements as well as image recovery from Fourier and Radon measurements, including a real-world scenario for magnetic resonance imaging (using the NYU -fastMRI dataset). Our main focus is on computing adversarial perturbations of the measurements that maximize the reconstruction error. Our empirical results reveal that standard end-to-end network architectures are not only surprisingly resilient against statistical noise, but also against adversarial perturbations. Remarkably, all considered networks are trained by common deep learning techniques, without adversarial defense strategies. We will also relate our results to the aspect of accuracy, which is discussed in the context of the 2021 AAPM Sparse-View CT Challenge. This is joint work with Ingo Gühring (TU Berlin), Maximilian März (Amazon), and Jan Macdonald (TU Berlin).