When Laplacian Scale Mixture Meets Three-Layer Transform: A Parametric Tensor Sparsity for Tensor Completion.

Area of Science:

• Data Science
• Machine Learning
• Signal Processing

Background:

• Tensor completion (TC) methods leverage tensor sparsity for data reconstruction.
• Existing approaches struggle with accurate rank estimation and hierarchical structure modeling.
• Low-rank tensor decomposition is a common but limited approach for measuring tensor sparsity.

Purpose of the Study:

• To propose a parametric tensor sparsity measure model for enhanced tensor completion.
• To address limitations in modeling hierarchical structures and accurate rank estimation.
• To develop a robust method for capturing complex sparsity patterns in tensors.

Main Methods:

• Introduced a parametric tensor sparsity measure using Laplacian scale mixture (LSM) modeling.
• Employed a three-layer transform (TLT) for factor subspace prior with Tucker decomposition.
• Utilized transform learning for adaptive depiction of deeper layer structured sparsity.
• Developed an alternating direction method of multipliers (ADMM)-based optimization algorithm.

Main Results:

• The proposed method, LSM-TLT, effectively models hierarchical tensor sparsity.
• Demonstrated superior performance in tensor completion tasks compared to state-of-the-art methods.
• Achieved significant improvements on datasets including RGB images, hyperspectral images (HSIs), and videos.

Conclusions:

• The LSM-TLT model provides a powerful and adaptive approach to tensor sparsity measurement.
• This method significantly enhances the accuracy and capability of tensor completion.
• The findings suggest broad applicability in various data analysis domains requiring tensor reconstruction.