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This paper introduces R-ItCUR, a novel algorithm designed to recover low-tubal-rank tensors from cross-concentrated sampling data even when contaminated by sparse, large outliers. By applying adaptive blockwise Welsch correction and operating directly on sampled blocks rather than full tensor reconstruction, the method achieves significant memory and computational savings while maintaining accuracy across synthetic, medical imaging, and seismic datasets. The work advances robust machine learning techniques specifically tailored for structured scientific computing environments where data corruption is a common challenge.
Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling
arXiv:2608.03928v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Information Theory (cs.IT); Machine Learning (cs.LG); Numerical Analysis (math.NA)
arXiv:2608.03928 [stat.ML]
(or arXiv:2608.03928v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2608.03928 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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