A Neural-Network-Based Convex Regularizer for Inverse Problems
Abstract
The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these shortcomings while retaining the boost in performance. In this work, we tackle this issue by revisiting regularizers that are the sum of convex-ridge functions. The gradient of such regularizers is parameterized by a neural network that has a single hidden layer with increasing and learnable activation functions. This neural network is trained within a few minutes as a multistep Gaussian denoiser. The numerical experiments for denoising, CT, and MRI reconstruction show improvements over methods that offer similar reliability guarantees.
Cite
@article{arxiv.2211.12461,
title = {A Neural-Network-Based Convex Regularizer for Inverse Problems},
author = {Alexis Goujon and Sebastian Neumayer and Pakshal Bohra and Stanislas Ducotterd and Michael Unser},
journal= {arXiv preprint arXiv:2211.12461},
year = {2023}
}