Multidimensional Imaging Data Completion via Weighted Three-Directional Minimax Concave Penalty Regularization.

Area of Science:

• Multidimensional data analysis
• Machine learning
• Optimization

Background:

• Tensor completion is crucial for reconstructing incomplete multidimensional data.
• Existing convex methods like nuclear norm minimization can over-penalize large singular values.
• Non-convex approaches offer potential for improved performance but present optimization challenges.

Purpose of the Study:

• To propose a novel non-convex tensor completion model for multidimensional data.
• To address the over-penalization issue common in convex tensor completion.
• To develop a robust and theoretically sound optimization algorithm for the proposed model.

Main Methods:

• Introduced a three-directional non-convex tensor rank surrogate regularized by the Minimax Concave Penalty (MCP) function.
• Developed an approximate convex model to handle non-convex optimization challenges.
• Implemented a convex Alternating Direction Method of Multipliers (ADMM)-based algorithm with convergence guarantees.

Main Results:

• The proposed MCP-regularized non-convex tensor completion model demonstrated superior performance.
• The method effectively mitigated the over-penalization of large singular values.
• Extensive experiments on real-world datasets confirmed the model's robustness and effectiveness compared to state-of-the-art methods.

Conclusions:

• The novel non-convex tensor completion model offers a significant advancement for multidimensional data analysis.
• The developed ADMM-based algorithm provides a reliable and efficient solution for non-convex tensor completion.
• This approach enhances the accuracy and robustness of reconstructing incomplete multidimensional datasets.