{"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/nf-ula-langevin-monte-carlo-with-normalizing","title":"NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problems","arxiv_id":"2304.08342","date":"2023-04-17","proceeding":null,"authors":["Ziruo Cai","Junqi Tang","Subhadip Mukherjee","Jinglai Li","Carola Bibiane Schönlieb","Xiaoqun Zhang"],"abstract":"Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving inverse problems have also been remarkably successful, due to their superior representation ability. In this work, we incorporate data-based models into a class of Langevin-based sampling algorithms for Bayesian inference in imaging inverse problems. In particular, we introduce NF-ULA (Normalizing Flow-based Unadjusted Langevin algorithm), which involves learning a normalizing flow (NF) as the image prior. We use NF to learn the prior because a tractable closed-form expression for the log prior enables the differentiation of it using autograd libraries. Our algorithm only requires a normalizing flow-based generative network, which can be pre-trained independently of the considered inverse problem and the forward operator. We perform theoretical analysis by investigating the well-posedness and non-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various image restoration problems such as image deblurring, image inpainting, and limited-angle X-ray computed tomography (CT) reconstruction. NF-ULA is found to perform better than competing methods for severely ill-posed inverse problems.","url_abs":"https://arxiv.org/abs/2304.08342v2","url_pdf":"https://arxiv.org/pdf/2304.08342v2.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":"nf-ula-langevin-monte-carlo-with-normalizing","repo_url":"https://github.com/caiziruo/nf-ula","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"ct-reconstruction","task_name":"CT Reconstruction"},{"task_slug":"computed-tomography-ct","task_name":"Computed Tomography (CT)"},{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"image-deblurring","task_name":"Image Deblurring"},{"task_slug":"image-inpainting","task_name":"Image Inpainting"},{"task_slug":"image-restoration","task_name":"Image Restoration"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2304.08342","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}