Efficient enhancement of low-rank tensor completion via thin QR decomposition

Area of Science:

• Data Science
• Numerical Analysis
• Computer Vision

Background:

• Low-rank tensor completion (LRTC) addresses missing data in tensors using low-rank properties.
• Core Tensor Nuclear Norm Minimization (CTNM) based on Tucker decomposition is a common LRTC method.
• Tucker decomposition-based CTNM methods suffer from high computational costs due to repeated Singular Value Decompositions (SVDs).

Purpose of the Study:

• To develop a more computationally efficient LRTC method.
• To improve the accuracy and performance of tensor completion algorithms.
• To reduce the complexity of existing CTNM methods.

Main Methods:

• Proposed a CTNM method based on thin QR decomposition (CTNM-QR).
• Introduced tensor auxiliary variables instead of matrices.
• Utilized thin QR decomposition for factor matrix solving, replacing SVD.

Main Results:

• CTNM-QR demonstrated lower computational complexity compared to SVD-based methods.
• The method achieved improved tensor completion accuracy and visualization.
• Experiments on synthetic data, color images, and MRI data confirmed superior performance.

Conclusions:

• CTNM-QR offers a more efficient and accurate approach to LRTC.
• The method effectively reduces computational burden while enhancing completion quality.
• This advancement is beneficial for applications involving large-scale tensor data.