Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling

• URL: http://arxiv.org/abs/2608.03928v2
• Date: Wed, 05 Aug 2026 01:23:20 GMT
• Title: Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling
• Abstract summary: Cross-concentrated sampling (t-CCS) bridges entrywise sampling and t-CUR slice-wise sampling by observing entries only within selected horizontal and lateral slices.<n>Existing t-CCS completion methods assume that the observations are free of gross corruption.<n>We study robust recovery of a third-order low-tubal-rank tensor from partial t-CCS observations contaminated by sparse, arbitrarily large outliers.
• Score: 17.954661155241272
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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