# Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems

## TL;DR

This paper introduces a method that replaces traditional regularization in inverse imaging problems with a denoising neural network, enabling flexible, high-quality reconstructions without retraining for each specific problem variation.

## Contribution

The authors propose using a denoising neural network as a proximal operator in variational methods, improving generalizability and reducing retraining needs in inverse imaging tasks.

## Key findings

- Achieved state-of-the-art results in image deconvolution and demosaicking.
- Demonstrated high generalizability across different problem settings.
- Reduced need for problem-specific retraining of neural networks.

## Abstract

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep learning approaches is their requirement for an expensive retraining whenever the specific problem, the noise level, noise type, or desired measure of fidelity changes. On the contrary, variational methods have a plug-and-play nature as they usually consist of separate data fidelity and regularization terms. In this paper we study the possibility of replacing the proximal operator of the regularization used in many convex energy minimization algorithms by a denoising neural network. The latter therefore serves as an implicit natural image prior, while the data term can still be chosen independently. Using a fixed denoising neural network in exemplary problems of image deconvolution with different blur kernels and image demosaicking, we obtain state-of-the-art reconstruction results. These indicate the high generalizability of our approach and a reduction of the need for problem-specific training. Additionally, we discuss novel results on the analysis of possible optimization algorithms to incorporate the network into, as well as the choices of algorithm parameters and their relation to the noise level the neural network is trained on.