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

2026-08-04

AI Summary

This work proposes the R-ItCUR algorithm to address robust low-tubal-rank recovery of partially observed third-order tensors corrupted by sparse, large-magnitude outliers under t-cross cross sampling (t-CCS). R-ItCUR is the first method to achieve such robust recovery within the t-CCS framework. It partitions the sampled tensor into two exterior blocks and an intersection block, integrates an adaptive Welsch correction to suppress outliers, and updates low-rank components via projected block-wise gradient descent—all without reconstructing the full tensor. By explicitly exploiting the sampling structure, the algorithm achieves high-accuracy recovery on synthetic data, cardiac MRI, and 3D seismic datasets, demonstrating strong robustness alongside substantial gains in computational and memory efficiency.

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.

Problem

• tensor completion
• low-tubal-rank
• cross-concentrated sampling
• robust recovery
• outlier corruption

Innovation

• robust tensor completion
• low-tubal-rank
• cross-concentrated sampling
• outlier suppression
• tensor-native algorithm