Deep neural networks provide excellent performance for inverse problems such
as denoising. However, neural networks can be sensitive to adversarial or
worst-case perturbations. This raises the question of whether such networks can
be trained efficiently to be worst-case robust. In this paper, we investigate
whether jittering, a simple regularization technique that adds isotropic
Gaussian noise during training, is effective for learning worst-case robust
estimators for inverse problems. While well studied for prediction in
classification tasks, the effectiveness of jittering for inverse problems has
not been systematically investigated. In this paper, we present a novel
analytical characterization of the optimal $\ell_2$-worst-case robust estimator
for linear denoising and show that jittering yields optimal robust denoisers.
Furthermore, we examine jittering empirically via training deep neural networks
(U-nets) for natural image denoising, deconvolution, and accelerated magnetic
resonance imaging (MRI). The results show that jittering significantly enhances
the worst-case robustness, but can be suboptimal for inverse problems beyond
denoising. Moreover, our results imply that training on real data which often
contains slight noise is somewhat robustness enhancing.

深度神经网络在反问题如降噪方面表现出色，但对抗性或最坏情况扰动敏感，本文研究了添加正态噪声的正则化技术 jittering 是否有效于学习最坏情况下鲁棒的反问题估计器。通过对线性降噪器进行分析表明，jittering 能够产生最佳的鲁棒降噪器。此外，通过对自然图像降噪、反卷积和磁共振成像（MRI）的深度神经网络（U-nets）进行实证研究，结果显示 jittering 显著提高了最坏情况下的鲁棒性，在除降噪之外的反问题中可能存在非最优情况，同时结果暗示通过对含有轻微噪声的真实数据进行训练，也能够提升鲁棒性。