这篇论文解决了逆问题模型在噪声变化时性能暴跌的痛点，用结构化的 DRO 替代傻均匀扰动，实验还发现它自动学出低秩算子。搞图像重建或鲁棒学习的可以细看。
该论文提出一种结构化分布鲁棒优化（DRO）框架，在逆问题学习重建中对抗训练与测试噪声分布不匹配的问题。与标准 Wasserstein DRO 对全部联合分布均匀扰动不同，该方法将不确定性集限制在符合测量过程的扰动子集上（如条件分布 P(Y|X)），更真实地建模前向算子与噪声模型。理论推导了强对偶性与显式最坏情况风险界，表明该框架等效于在重建算子 Lipschitz 常数上施加 Tikhonov 正则化。在去模糊和 sinogram-to-CT 重建实验上，该方法相比标准 DRO 和 MSE 基线，在鲁棒性、稳定性和可解释性上均有提升，且在线性设置下学习到的算子呈现低秩结构，可视为截断 SVD 的数据驱动变体。
A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training. Distributionally robust optimization (DRO) addresses this by optimizing against the worst-case distribution within a prescribed ambiguity set, but standard Wasserstein DRO perturbs the full joint distribution uniformly, which can be overly conservative and ignores the physics of the measurement process. We develop a structured DRO framework in which the ambiguity set is restricted to structured perturbations aligned with the data-acquisition process. This allows us to learn data-driven reconstruction operators that remain robust to distributional shifts. By constraining perturbations to subsets such as $P(Y|X)$, our framework models uncertainty in the forward operator and noise model more faithfully, accommodating any noise model expressible as a stochastic forward operator. We establish strong duality for this general formulation and derive explicit finite-dimensional dual representations for perturbations in the joint, marginal, and conditional distributions. A central result is an explicit worst-case risk bound that induces Tikhonov regularization on the Lipschitz constant of the reconstruction operator, and is less conservative relative to standard DRO for well-posed problems. Numerical experiments on deblurring and sinogram-to-CT reconstruction demonstrate improved robustness, stability, and interpretability over standard DRO and MSE baselines. In the linear setting, the learned operator becomes effectively low-rank, truncating at the intrinsic dimension of the data and recovering a data-driven analogue of truncated-SVD regularization.