Unfolded proximal neural networks for robust image Gaussian denoising

TL;DR

This paper introduces a unified framework for unfolded proximal neural networks (PNNs) tailored for Gaussian image denoising, leveraging optimization algorithms with learned parameters to improve robustness and efficiency.

Contribution

It proposes a novel PNN framework based on dual-FB and primal-dual Chambolle-Pock algorithms, incorporating acceleration and skip connections for enhanced denoising performance.

Findings

Accelerated PNNs improve denoising speed and quality.

The framework demonstrates robustness in image deblurring tasks.

Different learning strategies affect PNN robustness and efficiency.

Abstract

A common approach to solve inverse imaging problems relies on finding a maximum a posteriori (MAP) estimate of the original unknown image, by solving a minimization problem. In thiscontext, iterative proximal algorithms are widely used, enabling to handle non-smooth functions and linear operators. Recently, these algorithms have been paired with deep learning strategies, to further improve the estimate quality. In particular, proximal neural networks (PNNs) have been introduced, obtained by unrolling a proximal algorithm as for finding a MAP estimate, but over a fixed number of iterations, with learned linear operators and parameters. As PNNs are based on optimization theory, they are very flexible, and can be adapted to any image restoration task, as soon as a proximal algorithm can solve it. They further have much lighter architectures than traditional networks. In this article we propose a unified framework to build PNNs for the Gaussian denoising task, based on both the dual-FB and the primal-dual Chambolle-Pock algorithms. We further show that accelerated inertial versions of these algorithms enable skip connections in the associated NN layers. We propose different learning strategies for our PNN framework, and investigate their robustness (Lipschitz property) and denoising efficiency. Finally, we assess the robustness of our PNNs when plugged in a forward-backward algorithm for an image deblurring problem.