Solving Inverse Problems With Deep Neural Networks -- Robustness Included?

TL;DR

This paper investigates the robustness of deep neural networks used for inverse problems, revealing that standard architectures are more resilient to adversarial perturbations than previously thought, with comparisons to traditional methods.

Contribution

The study provides a comprehensive analysis of neural network robustness in inverse problems, including adversarial attacks and comparisons with total-variation minimization, highlighting unexpected resilience.

Findings

Neural networks show resilience against adversarial perturbations.

Comparison with total-variation minimization highlights robustness differences.

Networks trained with standard techniques are more robust than expected.

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. 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. The present article sheds new light on this concern, by conducting an extensive study of the robustness 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. A distinctive feature of our approach is the quantitative and qualitative comparison with total-variation minimization, which serves as a provably robust reference method. In contrast to previous findings, our results reveal that standard end-to-end network architectures are not only resilient against statistical noise, but also against adversarial perturbations. All considered networks are trained by common deep learning techniques, without sophisticated defense strategies.