Smooth Tensor Product for Tensor Completion.

Area of Science:

• Computer Vision
• Machine Learning
• Signal Processing

Background:

• Low-rank tensor completion (LRTC) is effective for incomplete visual data but often ignores local image/video smoothness.
• Existing LRTC methods struggle to exploit smoothness in the latent factor space and lack theoretical support.
• Previous approaches primarily focus on local smoothness within the original data space.

Purpose of the Study:

• To develop an innovative LRTC model that integrates global low-rank properties with local smoothness in factor tensors.
• To provide theoretical guarantees for the proposed smooth factor-based tensor completion.
• To improve the performance and reliability of visual data inpainting.

Main Methods:

• A novel tensor completion model is proposed, decomposing the tensor into two locally smooth factor tensors.
• An efficient alternating direction method of multipliers (ADMM) is employed for model optimization.
• Generalization error bounds for smooth factor-based tensor completion are derived.

Main Results:

• The proposed method demonstrates superior inpainting performance on color images, multispectral images, and videos compared to existing methods.
• The derived generalization error bounds are significantly tighter than current baselines.
• The approach exhibits low sensitivity to hyper-parameter settings, ensuring practical applicability.

Conclusions:

• The novel LRTC model effectively leverages both global low-rank structure and local factor smoothness for enhanced visual data recovery.
• The theoretical analysis provides a strong foundation for the effectiveness of smooth factor-based tensor completion.
• The method offers a robust, reliable, and convenient solution for various visual inpainting tasks.