{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:40:27Z","timestamp":1787337627720,"version":"3.56.0"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GZ 2047\/1"],"award-info":[{"award-number":["GZ 2047\/1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["390685813"],"award-info":[{"award-number":["390685813"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is controlled via introducing an auxiliary discretization dimension and choosing it in an adaptive fashion. We first show convergence for completely arbitrary compact forward operator and ground solution. Then the uncertainty of reaching the optimal convergence rate is quantified in a specific Bayesian-like environment. We conclude with numerical experiments.<\/jats:p>","DOI":"10.1137\/22m1506675","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T13:50:01Z","timestamp":1685109001000},"page":"591-615","source":"Crossref","is-referenced-by-count":3,"title":["Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise"],"prefix":"10.1137","volume":"11","author":[{"given":"Tim","family":"Jahn","sequence":"first","affiliation":[{"name":"Institute for Numerical Simulation, University of Bonn, 53115 Bonn, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,5,25]]},"reference":[{"key":"ref1","first-page":"1258","volume":"24","author":"Bakushinski\u0131 A.","year":"1984","journal-title":"Zh. Vychisl. Mat. i Mat. Fiz."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2011.01.016"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/5\/055009"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/060651884"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530510001564"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-19989-9_1"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1028674843"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1740-8"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974942"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/0917062"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/1034115"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02149761"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-020-01122-2"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drab098"},{"key":"ref15","volume-title":"Inverse Problems: Tikhonov Theory and Algorithms","author":"Ito K.","year":"2015"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac1775"},{"key":"ref17","unstructured":"T. Jahn , Discretisation-Adaptive Regularisation of Statistical Inverse Problems, preprint, arXiv:2204.14037, 2022."},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2021.2013881"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol57s35"},{"key":"ref20","series-title":"Appl. Math. Sci. 160","volume-title":"Statistical and Computational Inverse Problems","author":"Kaipio J.","year":"2006"},{"key":"ref21","first-page":"233","volume":"38","author":"Kindermann S.","year":"2011","journal-title":"Electron. Trans. Numer. Anal."},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2008.2.291"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aabe4f"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2019.1604546"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/1135065"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1515\/9783110286496"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2018047"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139994264476"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-06-01873-4"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2016.10.003"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1007\/BF00966239","volume":"7","author":"Morozov V. A.","year":"1966","journal-title":"Soviet Math. Dokl."},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1145\/321105.321114"},{"key":"ref33","unstructured":"K. Raik , Linear and Nonlinear Heuristic Regularisation for Ill-posed Problems, MA MSc., Ph.D. thesis, Universit\u00e4t Linz, Linz, Austria, 2020."},{"key":"ref34","first-page":"501","volume":"151","author":"Tikhonov A. N.","year":"1963","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8480-7"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1137\/0714044"},{"key":"ref37","volume-title":"All of Nonparametric Statistics","author":"Wasserman L.","year":"2006"}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1506675","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:21:37Z","timestamp":1787336497000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1506675"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,25]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6,30]]}},"alternative-id":["10.1137\/22M1506675"],"URL":"https:\/\/doi.org\/10.1137\/22m1506675","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,25]]}}}