Dictionary Learning With Low-Rank Coding Coefficients for Tensor Completion.

Area of Science:

• Data Science
• Machine Learning
• Signal Processing

Background:

• Tensor completion is crucial for reconstructing incomplete multidimensional data.
• Traditional methods often rely on predefined transform bases, limiting adaptability.
• Third-order tensor data, common in videos and images, presents unique completion challenges.

Purpose of the Study:

• To propose a novel tensor learning and coding model for third-order data completion.
• To develop a data-adaptive dictionary learning approach for tensor reconstruction.
• To enhance data completion accuracy and efficiency compared to existing methods.

Main Methods:

• A tensor learning and coding model is proposed for third-order data.
• A data-adaptive dictionary is learned from observations.
• The model minimizes the low-rankness of tensor slices containing coding coefficients.
• A multiblock proximal alternating minimization algorithm is developed for optimization.

Main Results:

• The learned dictionary offers more adaptive and accurate basis construction than predefined ones.
• Low-rankness of coding coefficients enables more effective linear combinations of dictionary features.
• The proposed algorithm demonstrates global convergence to a critical point.
• Experimental results on real-world data (videos, hyperspectral images, traffic data) show significant performance improvements over other tensor completion methods.

Conclusions:

• The novel tensor learning and coding model significantly enhances third-order data completion.
• Data-adaptive dictionary learning and low-rankness minimization are key advantages.
• The proposed method offers superior performance across various real-world datasets and evaluation metrics.