Unfolded Proximal Neural Networks for Robust Image Gaussian Denoising

Area of Science:

• Computational imaging
• Machine learning for image processing
• Optimization theory

Background:

• Inverse imaging problems commonly use Maximum a Posteriori (MAP) estimation via minimization.
• Iterative proximal algorithms are effective for non-smooth functions and linear operators in these tasks.
• Deep learning integration, specifically proximal neural networks (PNNs), has improved estimate quality.

Purpose of the Study:

• To propose a unified framework for building PNNs tailored for Gaussian denoising.
• To explore the benefits of accelerated inertial proximal algorithms for PNN architectures.
• To evaluate the robustness and efficiency of the proposed PNN framework.

Main Methods:

• Unrolling proximal algorithms (dual-FB and primal-dual Chambolle-Pock) into fixed-iteration neural networks.
• Implementing accelerated inertial versions to introduce skip connections in neural network layers.
• Developing and applying various learning strategies to the PNN framework.
• Assessing Lipschitz property for robustness and denoising performance.

Main Results:

• Demonstrated that accelerated inertial algorithms facilitate skip connections in PNN layers.
• Investigated different learning strategies, showing their impact on robustness and denoising efficiency.
• Validated the PNN framework's performance on Gaussian denoising tasks.
• Assessed the robustness of the developed PNNs within a forward-backward algorithm for image deblurring.

Conclusions:

• The proposed unified framework effectively builds PNNs for Gaussian denoising using proximal algorithms.
• Accelerated versions of these algorithms offer architectural advantages like skip connections.
• The PNNs exhibit promising robustness and efficiency, adaptable to various image restoration and deblurring tasks.