{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:25:49Z","timestamp":1747189549506,"version":"3.40.5"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2023,9,30]]},"DOI":"10.1137\/22m1525995","type":"journal-article","created":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T13:26:48Z","timestamp":1689946008000},"page":"670-692","source":"Crossref","is-referenced-by-count":1,"title":["A Note on the Regularity of Images Generated by Convolutional Neural Networks"],"prefix":"10.1137","volume":"5","author":[{"given":"Andreas","family":"Habring","sequence":"first","affiliation":[{"name":"Department of Mathematics and Scientific Computing, University of Graz, Graz, Austria."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2895-2375","authenticated-orcid":true,"given":"Martin","family":"Holler","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Scientific Computing, University of Graz, Graz, Austria."}]}],"member":"351","published-online":{"date-parts":[[2023,7,21]]},"reference":[{"volume-title":"Sobolev Spaces","year":"2003","author":"Adams R. A.","key":"ref1"},{"key":"ref2","series-title":"An Application-Oriented Introduction","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-7280-2","volume-title":"Linear Functional Analysis","author":"Alt H. W.","year":"2016"},{"key":"ref3","series-title":"Oxford Math. Monogr.","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of Bounded Variation and Free Discontinuity Problems","author":"Ambrosio L.","year":"2000"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492919000059","volume":"28","author":"Arridge S.","year":"2019","journal-title":"Acta Numer."},{"key":"ref6","first-page":"399","volume":"119","author":"Asim M.","year":"2020","journal-title":"Proc. Mach. Learn. Res. (PMLR)"},{"key":"ref7","first-page":"537","volume":"70","author":"Bora A.","year":"2017","journal-title":"Proc. Mach. Learn. Res. (PMLR)"},{"key":"ref8","series-title":"Oxford Lecture Ser. Math. Appl. 22","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198507840.001.0001","volume-title":"Gamma-Convergence for Beginners","author":"Braides A.","year":"2002"},{"key":"ref9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-01458-2","volume-title":"Mathematical Image Processing","author":"Bredies K.","year":"2018"},{"key":"ref10","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-70914-7","volume-title":"Functional Analysis, Sobolev Spaces and Partial Differential Equations","volume":"2","author":"Br\u00e9zis H.","year":"2011"},{"key":"ref11","series-title":"Radon Ser. Comput. Appl. Math. 9","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1515\/9783110226157.263","volume-title":"Theoretical Foundations and Numerical Methods for Sparse Recovery","author":"Chambolle A.","year":"2010"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s10851-019-00919-7","volume":"62","author":"Chambolle A.","year":"2020","journal-title":"J. Math. Imaging Vision"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/83.661187","volume":"7","author":"Chan T. F.","year":"1998","journal-title":"IEEE Trans. Image Process."},{"key":"ref15","series-title":"Grad. Stud. Math. 19","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/019","volume-title":"Partial Differential Equations","author":"Evans L. C.","year":"2010"},{"key":"ref16","first-page":"7368","volume":"162","author":"Genzel M.","year":"2022","journal-title":"Proc. Mach. Learn. Res. (PMLR)"},{"key":"ref17","volume-title":"Advances in Neural Information Processing Systems","volume":"27","author":"Goodfellow I.","year":"2014"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141000371150"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/21M1414978"},{"key":"ref21","volume-title":"Advances in Neural Information Processing Systems","volume":"31","author":"Hand P.","year":"2018"},{"key":"ref25","first-page":"769","volume-title":"Advances in Neural Information Processing Systems","volume":"21","author":"Jain V.","year":"2008"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"4509","DOI":"10.1109\/TIP.2017.2713099","volume":"26","author":"Jin K. H.","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref29","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1007\/s11263-020-01303-4","volume":"128","author":"Lempitsky V.","year":"2020","journal-title":"Int. J. Comput. Vis."},{"key":"ref31","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/181","volume-title":"A First Course in Sobolev Spaces","author":"Leoni G.","year":"2017"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"20150203","DOI":"10.1098\/rsta.2015.0203","volume":"374","author":"Mallat S.","year":"2016","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref33","volume-title":"Advances in Neural Information. Processing Systems","volume":"29","author":"Mao X.","year":"2016"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"Rudin L. I.","year":"1992","journal-title":"Phys. D"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"69","DOI":"10.3390\/jimaging9030069","volume":"9","author":"Skandarani Y.","year":"2023","journal-title":"J. Imaging"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"3142","DOI":"10.1109\/TIP.2017.2662206","volume":"26","author":"Zhang K.","year":"2017","journal-title":"IEEE Trans. Image Process."}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,12,17]],"date-time":"2023-12-17T14:56:25Z","timestamp":1702824985000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1525995"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,21]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,9,30]]}},"alternative-id":["10.1137\/22M1525995"],"URL":"https:\/\/doi.org\/10.1137\/22m1525995","relation":{},"ISSN":["2577-0187"],"issn-type":[{"type":"electronic","value":"2577-0187"}],"subject":[],"published":{"date-parts":[[2023,7,21]]}}}