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

This paper studies robust completion of third-order low-tubal-rank tensors from partial tensor cross-concentrated sampling (t-CCS) observations containing sparse, arbitrarily large outliers. It proposes Robust Iterative t-CUR (R-ItCUR), which splits the sampled cross into two exterior blocks and an intersection block, applies adaptive blockwise Welsch correction, and updates the low-rank component with projected blockwise gradient descent. The method operates directly on the sampled cross instead of reconstructing the full tensor during iterations. Experiments on synthetic tensors, cardiac MRI, and three-dimensional seismic data report accurate recovery and robustness to sparse gross corruption.