发表机构
University of California, San Diego; University of Michigan, Ann Arbor; Boston College; ShanghaiTech University; South China University of Technology; Tsinghua University; Huazhong University of Science and Technology（加州大学圣地亚哥分校; 密歇根大学安娜堡分校; 波士顿学院; 上海科技大学; 华南理工大学; 清华大学; 华中科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出两样本矩校准框架，利用不成对集合的共享损坏结构，通过秩感知信息状态和闭式矩辨识，实现校正的可辨识性评估与精度控制。
AI 中文摘要
多样观测的集合通常共享一种采集、处理、几何或通道损坏，而仅有一个不成对的干净参考集可用。对于跨观测共享的预设低维校正，观测集和干净参考集仅通过固定矩的响应来支持推断。我们将此问题表述为两样本矩校准，并报告一个秩感知信息状态，该状态结合了局部秩、缩放矩灵敏度、源分离协方差和矩兼容性残差。满秩给出局部矩可辨识性，而核方向在一阶上仍未解决。一个统一的线性化分离了观测集和参考集的不确定性。在协方差加权下，最弱的缩放奇异值决定最坏方向的渐近放大。对于跨观测共享的保向平面相似性校正，集成质心和非零三阶复矩在匹配总体和无裁剪假设下，给出平移、旋转和各向同性缩放的闭式全局总体辨识。受控验证测试了预测的$N^{-1}$和$\sigma_{\min}^{-2}$定律、高斯效率和区间覆盖率。有界应用报告了颜色校正输出质量、通道幅度响应校准，以及一个独立的配对几何去美化结果。因此，该框架报告缺失或弱信息，而不是将每个拟合的校正视为已辨识。
英文摘要
Collections of diverse observations often share one acquisition, processing, geometric, or channel corruption, while only an unpaired clean reference set is available. For a prescribed low-dimensional correction shared across observations, the observed and clean reference sets support inference only through the response of fixed moments. We formulate this problem as two-sample moment calibration and report a rank-aware information state combining local rank, scaled moment sensitivity, source-separated covariance, and a moment compatibility residual. Full rank gives local moment identifiability, whereas kernel directions remain unresolved to first order. A unified linearization separates observed-set and reference-set uncertainty. Under covariance weighting, the weakest scaled singular value determines worst-direction asymptotic amplification. For an orientation-preserving planar-similarity correction shared across observations, ensemble centroids and a nonzero third-order complex moment yield closed-form global population identification of translation, rotation, and isotropic scale under matched-population and no-clipping assumptions. Controlled validation tests the predicted $N^{-1}$ and $σ_{\min}^{-2}$ laws, Gaussian efficiency, and interval coverage. Bounded applications report color corrected-output quality, channel magnitude-response calibration, and a separate paired geometric de-beautification result. The framework therefore reports missing or weak information instead of treating every fitted correction as identified.
