A Neural-Network-Based Convex Regularizer for Inverse Problems

• URL: http://arxiv.org/abs/2211.12461v3
• Date: Fri, 25 Aug 2023 11:53:01 GMT
• Title: A Neural-Network-Based Convex Regularizer for Inverse Problems
• Authors: Alexis Goujon, Sebastian Neumayer, Pakshal Bohra, Stanislas Ducotterd, Michael Unser
• Abstract summary: Deep-learning methods to solve image-reconstruction problems have enabled a significant increase in reconstruction quality. These new methods often lack reliability and explainability, and there is a growing interest to address these shortcomings. 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.
• Score: 14.571246114579468
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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