{"0c5ab2bb1841f0df1cef81bab5d3cf99grigaud":{"DOI":"10.1093/imanum/drad002","ISBN":"","ISSN":"0272-4979","URL":"https://doi.org/10.1093/imanum/drad002","abstract":"Building on the well-known total variation, this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be adaptive (we speak of A-NID), i.e., the regularization varies during the iterates in order to incorporate prior information on the edges, deal with the evolution of the reconstruction and circumvent the limitations due to the nonconvexity of the proposed functionals. After a detailed analysis of the convergence and well-posedness of the method, the latter is validated by simulations performed on synthetic and real data on computerized tomography.","annote":"","author":[{"family":"Hahn","given":"Bernadette N"},{"family":"Rigaud","given":"Gaël"},{"family":"Schmähl","given":"Richard"}],"citation-label":"10.1093/imanum/drad002","collection-editor":[],"collection-title":"","container-author":[],"container-title":"IMA Journal of Numerical Analysis","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2023","02"]],"literal":"2023"},"event-place":"","id":"0c5ab2bb1841f0df1cef81bab5d3cf99grigaud","interhash":"ec0c2ad15f55791c070b356fd971816b","intrahash":"0c5ab2bb1841f0df1cef81bab5d3cf99","issue":"","issued":{"date-parts":[["2023","02"]],"literal":"2023"},"keyword":"exc2075 myown pn6 pn6-9 simtech updated","misc":{"eprint":"https://academic.oup.com/imajna/advance-article-pdf/doi/10.1093/imanum/drad002/49332831/drad002.pdf","issn":"0272-4979","doi":"10.1093/imanum/drad002"},"note":"drad002","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A class of regularizations based on nonlinear isotropic diffusion for inverse problems","type":"article-journal","username":"grigaud","version":"","volume":""},"46f0476d332064fbb5f1a0961a103122grigaud":{"DOI":"10.3934/ipi.2022061","ISBN":"","ISSN":"","URL":"https://doi.org/10.3934%2Fipi.2022061","abstract":"","annote":"","author":[{"family":"Arndt","given":"Clemens"},{"family":"Denker","given":"Alexander"},{"family":"Nickel","given":"Judith"},{"family":"Leuschner","given":"Johannes"},{"family":"Schmidt","given":"Maximilian"},{"family":"Rigaud","given":"Gael"}],"citation-label":"2022","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Inverse Problems and Imaging","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2022"]],"literal":"2022"},"event-place":"","id":"46f0476d332064fbb5f1a0961a103122grigaud","interhash":"d827685a803c1189b197c35b8f583c11","intrahash":"46f0476d332064fbb5f1a0961a103122","issue":"0","issued":{"date-parts":[["2022"]],"literal":"2022"},"keyword":"EXC2075 PN6-9 SimTech myown updated","misc":{"doi":"10.3934/ipi.2022061"},"note":"","number":"0","page":"0--0","page-first":"0","publisher":"American Institute of Mathematical Sciences (AIMS)","publisher-place":"","status":"","title":"In Focus - hybrid deep learning approaches to the HDC2021 challenge","type":"article-journal","username":"grigaud","version":"","volume":"0"},"67e6bed0c516c94cc12f5ccdec159db0grigaud":{"DOI":"10.1088/1361-6420/acb2ed","ISBN":"","ISSN":"","URL":"https://doi.org/10.1088%2F1361-6420%2Facb2ed","abstract":"","annote":"","author":[{"family":"Gödeke","given":"Janek"},{"family":"Rigaud","given":"Gaël"}],"citation-label":"G_deke_2023","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Inverse Problems","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2023","feb"]],"literal":"2023"},"event-place":"","id":"67e6bed0c516c94cc12f5ccdec159db0grigaud","interhash":"bf067aaf9935a678f03455bb81f2d5a3","intrahash":"67e6bed0c516c94cc12f5ccdec159db0","issue":"3","issued":{"date-parts":[["2023","feb"]],"literal":"2023"},"keyword":"EXC2075 PN6 PN6-9 SimTech myown updated","misc":{"doi":"10.1088/1361-6420/acb2ed"},"note":"","number":"3","page":"034004","page-first":"034004","publisher":"IOP Publishing","publisher-place":"","status":"","title":"Imaging based on Compton scattering: model uncertainty and data-driven reconstruction methods","type":"article-journal","username":"grigaud","version":"","volume":"39"}}