Robust Low-Tubal-Rank Tensor Completion Based on Tensor Factorization and Maximum Correntopy Criterion

Area of Science:

• Data Science
• Signal Processing
• Numerical Analysis

Background:

• Tensor completion aims to reconstruct tensors from partial observations, often leveraging low-rank properties.
• Low tubal rank is a key tensor property for characterizing inherent structure.
• Existing low-tubal-rank methods struggle with outliers due to reliance on second-order statistics.

Purpose of the Study:

• Propose a novel objective function for low-tubal-rank tensor completion robust to outliers.
• Develop efficient algorithms for optimizing the new objective function.
• Evaluate the performance and robustness of the proposed methods.

Main Methods:

• Introduced a new objective function for low-tubal-rank tensor completion utilizing correntropy as an error measure.
• Employed half-quadratic minimization to transform the optimization into a weighted low-tubal-rank tensor factorization problem.
• Developed two efficient algorithms for solving the transformed problem, including convergence and complexity analysis.

Main Results:

• The proposed correntropy-based objective function effectively mitigates the impact of outliers in tensor completion.
• The developed algorithms demonstrate efficient and stable convergence.
• Numerical experiments on synthetic and real data confirm the robust and superior performance compared to existing methods.

Conclusions:

• The proposed correntropy-based approach offers a robust solution for low-tubal-rank tensor completion, particularly in the presence of outliers.
• The efficient algorithms facilitate practical application of the robust tensor completion technique.
• This work advances the field of tensor completion by providing a more reliable method for data recovery.