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.

本文针对深度学习方法在图像重建领域中的应用进行了可靠性研究，通过对受压缩感知、傅里叶和 Radon 重建等问题进行深入分析并量化和定性地比较了深度学习和总变分模型，其结果表明，深度学习模型不仅对统计噪声有抗干扰能力，而且对对抗干扰也能够很好地处理。

使用深度神经网络解决反问题 -- 鲁棒性是否包含？

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

Accurate signal recovery or image reconstruction from indirect and possibly
undersampled data is a topic of considerable interest; for example, the
literature in the recent field of compressed sensing is already quite immense.
Inspired by recent breakthroughs in the development of novel first-order
methods in convex optimization, most notably Nesterov's smoothing technique,
this paper introduces a fast and accurate algorithm for solving common recovery
problems in signal processing. In the spirit of Nesterov's work, one of the key
ideas of this algorithm is a subtle averaging of sequences of iterates, which
has been shown to improve the convergence properties of standard
gradient-descent algorithms. This paper demonstrates that this approach is
ideally suited for solving large-scale compressed sensing reconstruction
problems as 1) it is computationally efficient, 2) it is accurate and returns
solutions with several correct digits, 3) it is flexible and amenable to many
kinds of reconstruction problems, and 4) it is robust in the sense that its
excellent performance across a wide range of problems does not depend on the
fine tuning of several parameters. Comprehensive numerical experiments on
realistic signals exhibiting a large dynamic range show that this algorithm
compares favorably with recently proposed state-of-the-art methods. We also
apply the algorithm to solve other problems for which there are fewer
alternatives, such as total-variation minimization, and convex programs seeking
to minimize the l1 norm of Wx under constraints, in which W is not diagonal.

本文介绍了一种基于凸优化中 Nesterov 技术的高精密快速算法，用于解决信号处理中的常见恢复问题，包括大规模压缩感知重建、全变差最小化等，并通过实验验证了其优越性。