Image Completion in Embedded Space Using Multistage Tensor Ring Decomposition.

Area of Science:

• Big Data Processing
• Multivariate Data Analysis
• Machine Learning

Background:

• Incomplete datasets are common in big data due to sensor limitations or errors.
• Recovering missing data is crucial for accurate analysis and efficient processing.
• Existing tensor completion methods face challenges with high missing ratios and noise.

Purpose of the Study:

• To propose a new tensor completion approach.
• To enhance data recovery in incomplete datasets using Tensor Ring decomposition.
• To address limitations of current methods in handling high missing data and noise.

Main Methods:

• Block Hankelization to transform incomplete tensors into higher-order tensors.
• Tensor Ring (TR) decomposition applied in an embedded space.
• Rank-incremental and multistage strategies for efficient TR decomposition.

Main Results:

• The proposed method demonstrates superior performance in tensor completion.
• Effectiveness is particularly notable for datasets with very high missing ratios.
• The approach shows robustness in handling noisy data.

Conclusions:

• The novel Tensor Completion approach using embedded Tensor Ring decomposition is effective.
• This method offers significant improvements over state-of-the-art algorithms.
• It provides a robust solution for big data processing with incomplete and noisy tensors.