{"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-generative-variational-model-for-inverse","title":"A Generative Variational Model for Inverse Problems in Imaging","arxiv_id":"2104.12630","date":"2021-04-26","proceeding":null,"authors":["Andreas Habring","Martin Holler"],"abstract":"This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative convolutional neural networks; it aims to generate the unknown from variables in a latent space via multi-layer convolutions and non-linear penalties, and penalizes an associated cost. In contrast to conventional neural-network-based approaches, however, the convolution kernels are learned directly from the measured data such that no training is required. The present work provides a mathematical analysis of the proposed model in a function space setting, including proofs for regularity and existence/stability of solutions, and convergence for vanishing noise. Moreover, in a discretized setting, a numerical algorithm for solving various types of inverse problems with the proposed model is derived. Numerical results are provided for applications in inpainting, denoising, deblurring under noise, super-resolution and JPEG decompression with multiple test images.","url_abs":"https://arxiv.org/abs/2104.12630v2","url_pdf":"https://arxiv.org/pdf/2104.12630v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-generative-variational-model-for-inverse","repo_url":"https://github.com/habring/generative_variational_reg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}