{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:14:53Z","timestamp":1787382893803,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly supported wavelets and boundary wavelets. We prove that the number of samples that must be acquired to ensure a stable and accurate reconstruction scales linearly with the dimension of the wavelet reconstruction spaces. We also provide numerical experiments that corroborate our theoretical results.<\/jats:p>","DOI":"10.1137\/140959365","type":"journal-article","created":{"date-parts":[[2015,4,2]],"date-time":"2015-04-02T11:58:24Z","timestamp":1427975904000},"page":"1196-1233","source":"Crossref","is-referenced-by-count":22,"title":["Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements"],"prefix":"10.1137","volume":"47","author":[{"given":"Ben","family":"Adcock","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anders C.","family":"Hansen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gitta","family":"Kutyniok","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jackie","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,4,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/130943431"},{"key":"atypb2","volume-title":"DAMTP Technical report 2011\/NA12","author":"Adcock B.","year":"2011"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-012-9221-x"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.07.004"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/29\/1\/015008"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/120895846"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2013.07.001"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-96-03255-8"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.11.011"},{"key":"atypb10","first-page":"219","volume-title":"Comm. Pure Appl. Math","author":"Cand\u00e8s E. J.","year":"2002"},{"key":"atypb11","first-page":"54","volume-title":"Appl. Comput. Harmon. Anal","author":"Cohen A.","year":"1993"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2010.11.033"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9298-9"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-003-0004-2"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691305000981"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1992-1134729-0"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.10.026"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1109\/18.119740"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2011.06.005"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/S003614109324649X"},{"key":"atypb22","volume-title":"A Wavelet Tour of Signal Processing","author":"Mallat S.","year":"2009","edition":"3"},{"key":"atypb23","first-page":"1","volume":"45","author":"Meyer Y.","year":"1987","journal-title":"Rend. Sem. Mat. Univ. Politec. Torino"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1109\/42.491416"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.12.025"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-99-05075-3"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1109\/5.843002"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/78.330352"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1109\/5.488704"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2003.809638"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140959365","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:16Z","timestamp":1787318776000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140959365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140959365"],"URL":"https:\/\/doi.org\/10.1137\/140959365","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}