Inverse problems aim to reconstruct unseen data from corrupted or perturbed measurements. While most work focuses on improving reconstruction quality, generalization accuracy and robustness are equally important, especially for safety-critical applications. Model-based architectures (MBAs), such as loop unrolling methods, are considered more interpretable and achieve better reconstructions. Empirical evidence suggests that MBAs are more robust to perturbations than black-box solvers, but the accuracy-robustness tradeoff in MBAs remains underexplored. In this work, we propose a simple yet effective training scheme for MBAs, called SGD jittering, which injects noise iteration-wise during reconstruction. We theoretically demonstrate that SGD jittering not only generalizes better than the standard mean squared error training but is also more robust to average-case attacks. We validate SGD jittering using denoising toy examples, seismic deconvolution, and single-coil MRI reconstruction. The proposed method achieves cleaner reconstructions for out-of-distribution data and demonstrates enhanced robustness to adversarial attacks.

翻译：逆问题旨在从受损或受扰的测量数据中重建未知数据。尽管大多数研究侧重于提升重建质量，泛化精度与鲁棒性同样至关重要，尤其在安全关键型应用中。基于模型的架构（如循环展开方法）被认为更具可解释性并能实现更优重建。实证研究表明，相较于黑盒求解器，基于模型的架构对扰动具有更强的鲁棒性，但其精度与鲁棒性之间的权衡关系仍未得到充分探索。本研究提出一种针对基于模型架构的简洁高效训练方案——随机梯度下降抖动，该方法在重建过程中逐迭代注入噪声。我们从理论上证明，随机梯度下降抖动不仅比标准均方误差训练具有更好的泛化能力，而且对平均情况攻击也表现出更强的鲁棒性。我们通过去噪玩具示例、地震反卷积和单线圈磁共振成像重建验证了随机梯度下降抖动的有效性。所提方法在分布外数据上实现了更清晰的重建结果，并展现出对对抗攻击的增强鲁棒性。