发表机构
University of Central Florida; Michigan State University; University of Kentucky; University of Texas MD Anderson Cancer Center（中佛罗里达大学; 密歇根州立大学; 肯塔基大学; 德克萨斯大学 MD 安德森癌症中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对受稀疏异常值污染的三阶低张量秩张量，提出鲁棒迭代t-CUR算法，在交叉集中采样下实现高效鲁棒补全，经多类数据验证其准确性与鲁棒性。
AI 中文摘要
张量交叉集中采样（t-CCS）仅在选定的水平切片和横向切片内观测元素，连接了元素级采样与t-CUR切片级采样。然而，现有t-CCS补全方法假设观测值无严重损坏。本研究针对受稀疏、任意大的异常值污染的三阶低张量秩张量，从部分t-CCS观测中研究其鲁棒恢复。我们提出张量原生算法鲁棒迭代t-CUR（R-ItCUR），该算法将采样张量交叉划分为两个外部块和一个交叉块，采用自适应块级Welsch校正抑制异常值，并通过投影块级梯度下降更新低秩分量。由于直接在采样交叉上操作，R-ItCUR在整个迭代过程中避免重建完整张量，从而大幅节省内存与计算量。在合成张量、心脏MRI数据及三维地震数据上的实验表明，该方法恢复准确且对稀疏严重异常值具有强鲁棒性，结果进一步凸显在鲁棒张量补全中显式利用交叉集中采样结构的重要性。
英文摘要
Tensor cross-concentrated sampling (t-CCS) bridges entrywise sampling and t-CUR slice-wise sampling by observing entries only within selected horizontal and lateral slices. Existing t-CCS completion methods, however, assume that the observations are free of gross corruption. In this work, we study robust recovery of a third-order low-tubal-rank tensor from partial t-CCS observations contaminated by sparse, arbitrarily large outliers. We propose Robust Iterative t-CUR (R-ItCUR), a tensor-native algorithm that partitions the sampled tensor cross into two exterior blocks and an intersection block, applies adaptive blockwise Welsch correction for outlier suppression, and updates the low-rank component through projected blockwise gradient descent. By operating directly on the sampled cross, R-ItCUR avoids reconstructing the full tensor throughout the iterations, resulting in substantial memory and computational savings. Experiments on synthetic tensors, cardiac MRI data, and three-dimensional seismic data demonstrate accurate recovery and strong robustness to sparse gross corruptions. The results further highlight the importance of explicitly exploiting the cross-concentrated sampling structure in robust tensor completion.
