{"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/solving-ill-posed-inverse-problems-using","title":"Solving ill-posed inverse problems using iterative deep neural networks","arxiv_id":"1704.04058","date":"2017-04-13","proceeding":null,"authors":["Jonas Adler","Ozan Öktem"],"abstract":"We propose a partially learned approach for the solution of ill posed inverse\nproblems with not necessarily linear forward operators. The method builds on\nideas from classical regularization theory and recent advances in deep learning\nto perform learning while making use of prior information about the inverse\nproblem encoded in the forward operator, noise model and a regularizing\nfunctional. The method results in a gradient-like iterative scheme, where the\n\"gradient\" component is learned using a convolutional network that includes the\ngradients of the data discrepancy and regularizer as input in each iteration.\nWe present results of such a partially learned gradient scheme on a non-linear\ntomographic inversion problem with simulated data from both the Sheep-Logan\nphantom as well as a head CT. The outcome is compared against FBP and TV\nreconstruction and the proposed method provides a 5.4 dB PSNR improvement over\nthe TV reconstruction while being significantly faster, giving reconstructions\nof 512 x 512 volumes in about 0.4 seconds using a single GPU.","url_abs":"http://arxiv.org/abs/1704.04058v2","url_pdf":"http://arxiv.org/pdf/1704.04058v2.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":"solving-ill-posed-inverse-problems-using","repo_url":"https://github.com/adler-j/learned_gradient_tomography","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"solving-ill-posed-inverse-problems-using","repo_url":"https://github.com/odlgroup/odl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MPL-2.0"}},{"paper_slug":"solving-ill-posed-inverse-problems-using","repo_url":"https://github.com/Zakobian/CT_framework_","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"solving-ill-posed-inverse-problems-using","repo_url":"https://github.com/bgris/odl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"solving-ill-posed-inverse-problems-using","repo_url":"https://github.com/hjahan58/learned_gradient_tomography","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":null,"task_name":"GPU"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1704.04058","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}