Multi-Dimensional Visual Data Restoration: Uncovering the Global Discrepancy in Transformed High-Order Tensor...

Area of Science:

• Multi-dimensional data analysis
• Tensor algebra
• Computer vision

Background:

• Existing high-order tensor algebraic frameworks generalize tensor singular value decomposition (t-SVD) but overlook discrepancies in singular value distribution.
• This oversight leads to suboptimal restoration of real-world multi-dimensional visual datasets.

Purpose of the Study:

• To develop a novel order-d tensor rank definition that accurately measures the low-rank nature of practical visual data tensors.
• To introduce a new tensor rank minimization regime for improved data restoration tasks.

Main Methods:

• Proposed a novel order-d tensor rank definition, termed the discrepant t-SVD rank, to capture discrepancies in singular value distribution.
• Introduced a nonconvex regularizer for a discrepant t-SVD rank minimization regime, offering a closed-form solution.
• Developed models for high-order tensor completion and robust principal component analysis based on the new regime.

Main Results:

• The proposed discrepant t-SVD rank effectively measures the low-rank property of visual data tensors.
• The new rank minimization regime provides a closed-form solution, avoiding issues with convex optimization.
• Developed methods outperform state-of-the-art competitors in restoring order-4 hyperspectral videos, color videos, and order-5 light field images.

Conclusions:

• The novel discrepant t-SVD rank and its minimization regime offer significant improvements in multi-dimensional data restoration.
• The proposed methods demonstrate effectiveness in various tensor restoration tasks, including hyperspectral tensor restoration.
• The study provides a more faithful measurement of high-order low-rank nature for practical visual data processing.