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

Area of Science:

• Data Science
• Applied Mathematics
• Signal Processing

Background:

• Low-tubal-rank tensor recovery is crucial but challenged by data corruption (damage, loss, outliers).
• Existing methods struggle with simultaneous data damage and loss, often requiring clean data for prior information generation.
• Subspace prior information is vital but its accurate quantification remains a challenge.

Purpose of the Study:

• To propose a generalized subspace coupling (GSC) scheme for robust low-tubal-rank tensor completion.
• To address limitations of existing methods in handling simultaneously damaged and lost tensor data.
• To develop a robust method that does not require clean data for subspace prior information generation.

Main Methods:

• Introduced a generalized subspace coupling (GSC) scheme with a novel tool for prior subspace accuracy quantification.
• Formulated a robust low-tubal-rank tensor completion problem to recover tensors from noisy, incomplete data.
• Developed a symmetric Gauss-Seidel-based alternating direction method of multipliers (sGS-ADMM) for model optimization with guaranteed convergence.

Main Results:

• The proposed GSC scheme demonstrates superior performance in recovering low-tubal-rank tensors from corrupted data.
• Theoretical analysis confirms exact tensor recovery under significantly weaker incoherence conditions than previous methods.
• Experimental validation on facial images, medical scans, and video sequences shows significant improvements over existing techniques.

Conclusions:

• The developed GSC scheme offers a robust and effective solution for low-tubal-rank tensor completion, even with damaged and noisy data.
• The method advances the field by enabling accurate recovery under less stringent conditions and without requiring pristine data.
• The sGS-ADMM optimization ensures efficient and reliable model performance across diverse applications.