Generalized Subspace Coupling Approach for Robust Low-Tubal-Rank Tensor Completion

The field of low-tubal-rank tensor recovery, especially with subspace prior information, has recently garnered significant attention. However, existing methods encounter limitations when dealing with tensor data affected by simultaneous damage and loss. Moreover, they frequently necessitate clean (with no outliers) data to generate subspace prior information, which presents practical challenges. Addressing these issues, this article proposes a generalized subspace coupling (GSC) scheme, equipped with a novel tool to quantify the accuracy of the prior subspace. Building upon this foundation, we delve into the robust low-tubal-rank tensor completion problem, aiming to recover a low-tubal-rank tensor from partially observed data corrupted by sparse noise. Importantly, we theoretically demonstrate that the proposed method achieves exact tensor recovery under significantly weaker incoherence conditions compared to those previously suggested. Additionally, to optimize the proposed model, we design a symmetric Gauss-Seidel-based alternating direction method of multipliers (sGS-ADMM) with guaranteed convergence. Experiments conducted on various datasets, including facial images, medical scans, and video sequences, validate the superiority of our model over existing competitors in both qualitative and quantitative assessments.