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.

在这篇文章中，我们提出了一个统一的框架来构建用于高斯降噪任务的近端神经网络（PNNs），该框架基于双重 - 投影算法和原 - 对偶 Chambolle-Pock 算法。我们还展示了这些算法的加速惯性版本如何在关联的神经网络层中实现跳跃连接。我们为 PNN 框架提供了不同的学习策略，并研究了它们的鲁棒性（利普希茨性质）和降噪效率。最后，我们评估了将我们的 PNNs 插入图像去模糊问题的前向 - 后向算法时的鲁棒性。