Robust Tensor Completion via Capped Frobenius Norm.

Area of Science:

• Data Science
• Signal Processing
• Numerical Analysis

Background:

• Tensor completion (TC) restores missing tensor entries using low-rank structures.
• Existing methods excel in either Gaussian or impulsive noise but not both.
• Frobenius-norm methods are good for Gaussian noise, while l_p-norm methods handle impulsive noise.

Purpose of the Study:

• Develop a tensor completion algorithm robust to both Gaussian and impulsive noise.
• Improve recovery accuracy compared to existing methods in mixed noise conditions.
• Provide a parameter-free approach for enhanced tensor completion.

Main Methods:

• Utilized a capped Frobenius norm to mitigate outliers, adapting its bound via normalized median absolute deviation.
• Employed half-quadratic theory to transform the non-convex problem into a tractable multivariable convex optimization problem.
• Applied proximal block coordinate descent (PBCD) for efficient optimization and proved algorithm convergence.

Main Results:

• The capped Frobenius norm effectively restrains outliers, outperforming l_p-norm methods with contaminated data.
• Achieved comparable accuracy to Frobenius norm methods in Gaussian noise without parameter tuning.
• Demonstrated superior recovery performance over state-of-the-art algorithms in real-world image and video experiments.

Conclusions:

• The proposed capped Frobenius norm tensor completion method offers robust performance across different noise types.
• The PBCD algorithm ensures convergence, making the method reliable for practical applications.
• This approach significantly advances tensor completion techniques for noisy data scenarios.