{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-neural-network-based-convex-regularizer-for","title":"A Neural-Network-Based Convex Regularizer for Inverse Problems","arxiv_id":"2211.12461","date":"2022-11-22","proceeding":null,"authors":["Alexis Goujon","Sebastian Neumayer","Pakshal Bohra","Stanislas Ducotterd","Michael Unser"],"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.","url_abs":"https://arxiv.org/abs/2211.12461v3","url_pdf":"https://arxiv.org/pdf/2211.12461v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-neural-network-based-convex-regularizer-for","repo_url":"https://github.com/axgoujon/convex_ridge_regularizers","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"a-neural-network-based-convex-regularizer-for","repo_url":"https://github.com/astro-informatics/quantifai","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-reconstruction","task_name":"Image Reconstruction"},{"task_slug":"mri-reconstruction","task_name":"MRI Reconstruction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2211.12461","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}