Tensor Completion Using Bilayer Multimode Low-Rank Prior and Total Variation.

Area of Science:

• Tensor Decomposition
• Multilinear Algebra
• Machine Learning

Background:

• Low-rank (LR) tensor recovery is crucial in various fields.
• Existing methods often struggle with multiorientational correlations and local structures.

Purpose of the Study:

• To propose a novel bilayer low-rankness measure for enhanced tensor recovery.
• To develop models that capture both global and local low-rank properties in N-way tensors (N ≥ 3).

Main Methods:

• Encoding global low rankness via LR matrix factorizations (MFs) on all-mode matricizations.
• Introducing a double nuclear norm scheme to explore second-layer low rankness in decomposed subspaces.
• Utilizing a block successive upper-bound minimization (BSUM) algorithm for optimization.

Main Results:

• The proposed methods successfully model multiorientational correlations in arbitrary N-way tensors.
• Experimental results demonstrate superior recovery of LR tensors from fewer samples compared to counterparts.
• Convergence analysis shows the algorithm converges to coordinatewise minimizers under mild conditions.

Conclusions:

• The novel bilayer low-rankness measure and associated models offer a significant advancement in LR tensor recovery.
• The approach effectively addresses limitations of existing methods by capturing complex tensor structures.
• The BSUM algorithm provides a robust and convergent solution for the proposed optimization problems.