Unrolling Plug-and-Play Gradient Graph Laplacian Regularizer for Image Restoration.

Area of Science:

• Computer Vision
• Machine Learning
• Signal Processing

Background:

• Generic deep learning (DL) networks for image restoration lack mathematical interpretability and robustness.
• They require extensive training data and large parameter sets.
• Covariate shift poses a significant challenge for current DL models.

Purpose of the Study:

• To develop interpretable deep learning networks for image restoration.
• To address the limitations of generic DL models in terms of interpretability, data requirements, and robustness.
• To introduce a novel approach combining graph-based optimization with deep learning.

Main Methods:

• Formulated a convex quadratic programming (QP) problem with a novel gradient graph Laplacian regularizer (GGLR) prior for piecewise planar (PWP) signal reconstruction.
• Designed a family of Alternating Direction Method of Multipliers (ADMM) algorithms by introducing auxiliary variables to solve the QP problem.
• Unrolled ADMM algorithms into variable-complexity feedforward networks with graph learning modules, inspired by self-attention mechanisms.

Main Results:

• Unrolled networks achieved competitive image restoration quality compared to generic DL networks.
• The proposed networks utilized a fraction of the parameters of generic DL models.
• Demonstrated improved robustness against covariate shift in image restoration tasks.

Conclusions:

• The developed interpretable unrolled networks offer a viable alternative to generic DL models for image restoration.
• The approach successfully integrates mathematical interpretability with deep learning performance.
• Future work can explore more complex graph structures and regularization priors for enhanced performance.