Bayesian Low Rank Tensor Ring for Image Recovery.

Area of Science:

• Data Science
• Image Processing
• Machine Learning

Background:

• Low rank tensor ring (TR) based data recovery is crucial for reconstructing missing image data.
• Existing TR completion methods often use alternating least squares with predefined ranks, risking overfitting with limited measurements.
• Determining optimal TR ranks remains a challenge in low-rank tensor approximation.

Purpose of the Study:

• To develop a Bayesian low rank tensor ring completion method for robust image recovery.
• To automatically learn the low-rank structure of data without manual parameter tuning.
• To improve recovery accuracy, especially when dealing with sparse measurements.

Main Methods:

• A Bayesian approach is employed for low rank tensor ring completion.
• A multiplicative interaction model is developed for TR approximation.
• Sparsity-inducing hierarchical priors are applied to core factors for enhanced structure learning.

Main Results:

• The proposed Bayesian TR method effectively learns low-rank structures automatically.
• TR ranks are determined through Bayesian inference, eliminating the need for manual setting.
• The method demonstrates superior performance compared to state-of-the-art techniques in recovery accuracy.
• Experiments on synthetic data, real images, and the YaleFace dataset validate the findings.

Conclusions:

• The Bayesian low rank tensor ring completion method offers a parameter-free and accurate solution for image recovery.
• It effectively addresses the overfitting issue common in traditional TR completion methods.
• This approach advances the field of low-rank tensor approximation for image data.