To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion.

Area of Science:

• Computer Vision
• Data Science
• Applied Mathematics

Background:

• Tensor train (TT) representation is successful in visual data completion.
• Tensor folding, often used with TT, disrupts data structure and causes local information loss.

Purpose of the Study:

• To preserve local information in visual data during tensor train completion.
• To develop a computationally efficient and accurate TT completion method.

Main Methods:

• Avoiding tensor folding to maintain original data structure.
• Utilizing graph information to regularize local similarity between data entries.
• Decomposing the completion problem into sub-problems for TT core fibers to reduce computational complexity.
• Employing a sparsity-promoting probabilistic model with a generalized inverse Gaussian (GIG) prior and mean-field approximation for inference.

Main Results:

• The proposed method successfully preserves local information in visual data.
• The decomposition strategy significantly reduces computational complexity compared to traditional TT methods.
• The probabilistic model avoids heavy parameter tuning and promotes sparsity.
• Experiments demonstrate superior performance on synthetic and real-world visual data.

Conclusions:

• The novel TT completion method effectively preserves local data structure.
• The approach offers a more efficient and robust solution for visual data completion tasks.
• This work advances TT representation applications in image and video processing.