Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling
Organizations: School of Data, Mathematical, and Statistical Sciences and Department of Computer Science, University of Central Florida, Orlando, FL 32816, USA · Department of Computational Mathematics, Science, and Engineering and Department of Mathematics, Michigan State University, East Lansing, MI 48840, USA · Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA · Department of Imaging Physics, Department of Biostatistics, Department of Breast Imaging, and Institute for Data Science in Oncology, University of Texas MD Anderson Cancer Center, Houston, TX 77054, USA
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.