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

arXiv: https://arxiv.org/abs/2608.03928 · HTML: https://mlsanity.com/paper/2608.03928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 51 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 27 of 27)

- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [A large annotated medical image dataset for the development and evaluation of segmentation algorithms](https://mlsanity.com/paper/1902.09063/) (2019)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent](https://mlsanity.com/paper/2005.08898/) (2020)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Fast Algorithms for Robust PCA via Gradient Descent](https://mlsanity.com/paper/1605.07784/) (2016)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration](https://mlsanity.com/paper/1709.00192/) (2017)
- [Accelerated Alternating Projections for Robust Principal Component Analysis](https://mlsanity.com/paper/1711.05519/) (2017)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Robust Spectral Compressed Sensing via Structured Matrix Completion](https://mlsanity.com/paper/1304.8126/) (2013)
- [Nearly-optimal Robust Matrix Completion](https://mlsanity.com/paper/1606.07315/) (2016)
- [Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions](https://mlsanity.com/paper/2103.11037/) (2021)
- [Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling](https://mlsanity.com/paper/2208.09723/) (2022)
- [Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion](https://mlsanity.com/paper/2204.03316/) (2022)
- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [Robust Low-tubal-rank Tensor Completion based on Tensor Factorization and Maximum Correntopy Criterion](https://mlsanity.com/paper/2010.11740/) (2020)
- [On the Robustness of Cross-Concentrated Sampling for Matrix Completion](https://mlsanity.com/paper/2401.15566/) (2024)
- [Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery](https://mlsanity.com/paper/2410.16826/) (2024)
- [Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent](https://mlsanity.com/paper/2406.07409/) (2024)
- [Guaranteed Sampling Flexibility for Low-tubal-rank Tensor Completion](https://mlsanity.com/paper/2406.11092/) (2024)
- [Deeply Learned Robust Matrix Completion for Large-scale Low-rank Data Recovery](https://mlsanity.com/paper/2501.00677/) (2024)
- [Optimal Matrix-Mimetic Tensor Algebras via Variable Projection](https://mlsanity.com/paper/2406.06942/) (2024)
- [Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent](https://mlsanity.com/paper/2501.01696/) (2025)

## Abstract (arXiv)

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.