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Tensor Completion via Complementary Global, Local, and Nonlocal Priors.

Xi-Le Zhao, Jing-Hua Yang, Tian-Hui Ma

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|December 31, 2021

Summary

This summary is machine-generated.

This study introduces a novel tensor completion framework that unifies global, local, and nonlocal priors for visual data. This integrated approach enhances performance by enabling priors to collaborate effectively.

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Area of Science:

Computer Vision
Data Science
Signal Processing

Background:

Completing missing data in multidimensional visual datasets is challenging due to the ill-posed nature of the problem.
Existing methods often rely on one or two types of data priors: global tensor low-rankness, local properties, or nonlocal self-similarity (NSS).
A unified approach leveraging multiple priors concurrently could potentially improve data completion performance.

Purpose of the Study:

To develop a novel tensor completion framework that integrates global, local, and nonlocal priors.
To investigate the collaborative benefits of combining these diverse priors for enhanced data completion.
To propose an efficient algorithm for solving the unified tensor completion model.

Main Methods:

Formulated a tensor completion framework utilizing tensor train (TT) rank for global correlation.
Incorporated two Plug-and-Play (PnP) denoisers: a convolutional neural network (CNN) for local details and color block-matching and 3D filtering (CBM3D) for NSS.
Designed a proximal alternating minimization algorithm to solve the proposed model, with established convergence guarantees.

Main Results:

The unified framework successfully integrates global, local, and nonlocal priors.
The proposed proximal alternating minimization algorithm efficiently solves the model.
Extensive experiments demonstrate that the collaborative use of priors leads to state-of-the-art performance in data completion, both quantitatively and qualitatively.

Conclusions:

Concurrent utilization of global, local, and nonlocal priors in a unified framework significantly enhances multidimensional visual data completion.
The proposed PnP-based tensor completion model and its associated algorithm offer an effective solution.
The findings suggest that synergistic integration of diverse data priors is a promising direction for tackling ill-posed problems in visual data processing.