{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:37:55Z","timestamp":1787323075493,"version":"build-2736575974"},"reference-count":50,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"Danish Council for Independent Research - Natural Sciences","award":["4002-00123"],"award-info":[{"award-number":["4002-00123"]}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["W1214-N15"],"award-info":[{"award-number":["W1214-N15"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P26687"],"award-info":[{"award-number":["P26687"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We consider a problem of quantitative static elastography, the estimation of the Lam\u00e9 parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam\u00e9 parameters from displacement data simulating a static elastography experiment are presented.<\/jats:p>","DOI":"10.1137\/17m1154461","type":"journal-article","created":{"date-parts":[[2018,5,17]],"date-time":"2018-05-17T15:05:42Z","timestamp":1526569542000},"page":"1268-1293","source":"Crossref","is-referenced-by-count":25,"title":["Lam\u00e9 Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems"],"prefix":"10.1137","volume":"11","author":[{"given":"Simon","family":"Hubmer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ekaterina","family":"Sherina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Neubauer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Otmar","family":"Scherzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,5,17]]},"reference":[{"key":"atypb1","unstructured":"R. A. Adams and J. J. F. Fournier,\n                      Sobolev Spaces\n                      , Pure Appl. Math., Academic Press, Amsterdam, 2003."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160120405"},{"key":"atypb3","unstructured":"M. S. Aln\\aes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells,\n                      The FEniCS Project Version\n                      1.5, Arch. Numer. Softw., 3 (2015), 100,https:\/\/doi.org\/10.11588\/ans.2015.100.20553."},{"key":"atypb4","first-page":"1353","volume":"32","author":"Bakushinskii A. B.","year":"1992","journal-title":"Comput. Math. Math. Phys."},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"A. B. Bakushinsky and M. Y. Kokurin,\n                      Iterative Methods for Approximate Solution of Inverse Problems\n                      , Math. Appl. 577, Springer, Dordrecht, The Netherlands, 2004.","DOI":"10.1007\/978-1-4020-3122-9"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/30\/12\/125004"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1515\/jip-2012-0091"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2012.03.005"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21453"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/20\/1\/017"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/52\/6\/003"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"atypb13","unstructured":"P. G. Ciarlet,\n                      Mathematical Elasticity: Three-Dimensional Elasticity\n                      , Math. Elast. 1, North-Holland, Amsterdam, 1993,https:\/\/books.google.at\/books?id=sQiOzyTOJXUC."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/57\/3\/R35"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/45\/6\/309"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"H. W. Engl, M. Hanke, and A. Neubauer,\n                      Regularization of Inverse Problems\n                      , Kluwer, Dordrecht, The Netherlands, 1996.","DOI":"10.1007\/978-94-009-1740-8"},{"key":"atypb17","unstructured":"L. C. Evans,\n                      Partial Differential Equations\n                      , Grad. Stud. Math., AMS, Providence, RI, 1998,https:\/\/books.google.at\/books?id=5Pv4LVB_m8AC."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/3\/020"},{"key":"atypb19","unstructured":"D. Gilbarg and N. S. Trudinger,\n                      Elliptic Partial Differential Equations of Second Order\n                      , Grundlehren Math. Wiss. 224, Springer, Berlin, 1998,https:\/\/books.google.at\/books?id=PfA_AQAAIAAJ."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/4\/045010"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050158"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1080\/174159797088027646"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2018007"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aa7ac7"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2007.12.016"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/19\/6\/051"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/32\/10\/104005"},{"key":"atypb28","doi-asserted-by":"crossref","unstructured":"B. Kaltenbacher, A. Neubauer, and O. Scherzer,\n                      Iterative Regularization Methods for Nonlinear Ill-Posed Problems\n                      , Walter de Gruyter, Berlin, 2008,https:\/\/doi.org\/10.1515\/9783110208276.","DOI":"10.1515\/9783110208276"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/25\/6\/065003"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/32\/8\/085001"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.4171\/JST\/88"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/6\/065009"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1080\/17415977.2015.1132713"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1109\/58.741427"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/2\/018"},{"key":"atypb36","unstructured":"W. C. H. McLean,\n                      Strongly Elliptic Systems and Boundary Integral Equations\n                      , Cambridge University Press, Cambridge, 2000."},{"key":"atypb37","doi-asserted-by":"crossref","unstructured":"J. Necas,\n                      Direct Methods in the Theory of Elliptic Equations\n                      , Springer Monogr. Math., Springer, Berlin, Heidelberg, 2011.","DOI":"10.1007\/978-3-642-10455-8"},{"key":"atypb38","first-page":"372","volume":"27","author":"Nesterov Y.","year":"1983","journal-title":"Sov. Math. Dokl."},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1515\/jiip-2016-0060"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/49\/13\/013"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/19\/2\/304"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1109\/58.285465"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1177\/016173469101300201"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-1943-0_23"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1080\/01630569608816691"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(99)00413-7"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/1\/017"},{"key":"atypb48","doi-asserted-by":"crossref","unstructured":"T. Schuster, B. Kaltenbacher, B. Hofmann, and K. S. Kazimierski,\n                      Regularization Methods in Banach Spaces\n                      , Radon Ser. Comput. Appl. Math., De Gruyter, Boston, 2012.","DOI":"10.1515\/9783110255720"},{"key":"atypb49","unstructured":"T. Valent,\n                      Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data\n                      , Springer Tracts Nat. Philos., Springer, New York, 2013."},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/31\/3\/035005"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1154461","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:40:36Z","timestamp":1787319636000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1154461"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":50,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1154461"],"URL":"https:\/\/doi.org\/10.1137\/17m1154461","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}