Multilayer Sparsity-Based Tensor Decomposition for Low-Rank Tensor Completion.

Area of Science:

• Multidimensional Data Analysis
• Machine Learning
• Signal Processing

Background:

• Existing tensor completion (TC) methods struggle to characterize complex low-rank (LR) structures.
• Tensors often contain hierarchical knowledge and implicit sparsity that current models fail to capture.
• The need for advanced tensor decomposition techniques for accurate data reconstruction and analysis.

Purpose of the Study:

• To propose a novel multilayer sparsity-based tensor decomposition (MLSTD) for low-rank tensor completion (LRTC).
• To effectively depict complex hierarchical knowledge and implicit sparsity within tensor data.
• To improve the characterization of low-rank structures in tensor completion.

Main Methods:

• Developed a multilayer sparsity-based tensor decomposition (MLSTD) model.
• Utilized the CANDECOMP/PARAFAC (CP) model for tensor decomposition into rank-1 tensors.
• Incorporated a novel third-layer sparsity insight using self-adaptive low-rank matrix factorization (LRMF).
• Designed an alternating direction method of multipliers (ADMM) algorithm for MLSTD minimization.

Main Results:

• The proposed MLSTD model effectively encodes structured sparsity through a multiple-layer representation.
• Experiments on RGB images, hyperspectral images (HSIs), and videos demonstrated superior performance compared to state-of-the-art methods.
• The method accurately reconstructs low-rank tensor structures by progressively describing sparsity.

Conclusions:

• MLSTD provides a superior framework for low-rank tensor completion by capturing intricate sparsity patterns.
• The proposed method offers enhanced performance in reconstructing and analyzing complex, high-dimensional data.
• MLSTD is a promising approach for applications involving image and video processing.