Enhanced Sparsity Prior Model for Low-Rank Tensor Completion.

Area of Science:

• Data Science
• Machine Learning
• Signal Processing

Background:

• Conventional tensor completion (TC) relies on global sparsity assumptions, which are often insufficient for low-rank tensor recovery, especially with missing data.
• Existing methods struggle with the inherent complexity and missing elements in real-world tensor data.

Purpose of the Study:

• To develop an enhanced sparsity prior model for low-rank tensor completion (LRTC) by integrating both local and global sparsity information.
• To improve the accuracy and efficiency of recovering low-rank tensor data with significant missing entries.

Main Methods:

• A doubly weighted nuclear norm strategy is employed to capture the global sparsity prior across tensor modes.
• A novel factor gradient sparsity prior is introduced within the Tucker decomposition framework to model local smoothness and piecewise structures in latent tensors.
• The proposed local sparsity prior does not require minimizing the tensor rank.

Main Results:

• The enhanced model demonstrates superior performance compared to state-of-the-art techniques on synthetic datasets.
• Experiments on real-world hyperspectral images and face modeling data validate the model's effectiveness.
• The proposed method achieves higher prediction accuracy and improved computational efficiency.

Conclusions:

• Integrating local and global sparsity priors offers a more robust approach to low-rank tensor completion.
• The factor gradient sparsity prior effectively captures local tensor structures, enhancing recovery performance.
• The proposed LRTC method provides a significant advancement for applications involving complex, incomplete tensor data.