{"id":"https://openalex.org/W3136642988","doi":"https://doi.org/10.1090/mcom/3683","title":"On an inverse problem of nonlinear imaging with fractional damping","display_name":"On an inverse problem of nonlinear imaging with fractional damping","publication_year":2021,"publication_date":"2021-07-28","ids":{"openalex":"https://openalex.org/W3136642988","doi":"https://doi.org/10.1090/mcom/3683","mag":"3136642988"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3683","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3683","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.08965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011058927","display_name":"Barbara Kaltenbacher","orcid":"https://orcid.org/0000-0002-3295-6977"},"institutions":[{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Barbara Kaltenbacher","raw_affiliation_strings":["Department of Mathematics, Alpen-Adria-Universit\u00c3\u00a4t Klagenfurt, Universitatsstrasse 65-67, 9020 Klagenfurt Austria","Department of Mathematics, Alpen-Adria-Universit\u00e4t Klagenfurt, Universitatsstrasse 65-67, 9020 Klagenfurt Austria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Alpen-Adria-Universit\u00c3\u00a4t Klagenfurt, Universitatsstrasse 65-67, 9020 Klagenfurt Austria","institution_ids":["https://openalex.org/I4210166741"]},{"raw_affiliation_string":"Department of Mathematics, Alpen-Adria-Universit\u00e4t Klagenfurt, Universitatsstrasse 65-67, 9020 Klagenfurt Austria","institution_ids":["https://openalex.org/I4210166741"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088154743","display_name":"William Rundell","orcid":"https://orcid.org/0000-0001-9579-2183"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William Rundell","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas 77843","\u2020Texas A&M University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77843","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"\u2020Texas A&M University","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011058927"],"corresponding_institution_ids":["https://openalex.org/I4210166741"],"apc_list":null,"apc_paid":null,"fwci":0.9127,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6867437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"91","issue":"333","first_page":"245","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6883423924446106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6470469236373901},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5555235147476196},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5537360310554504},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5381186604499817},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.5118009448051453},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4549526572227478},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.44552719593048096},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.43462252616882324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4290471374988556},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.42287513613700867},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1702660322189331},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1067538857460022}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6883423924446106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6470469236373901},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5555235147476196},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5537360310554504},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5381186604499817},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5118009448051453},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4549526572227478},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.44552719593048096},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43462252616882324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4290471374988556},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.42287513613700867},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1702660322189331},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1067538857460022},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3683","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3683","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2103.08965","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.08965","pdf_url":"https://arxiv.org/pdf/2103.08965","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3136642988","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2103.08965v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2103.08965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.08965","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.08965","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.08965","pdf_url":"https://arxiv.org/pdf/2103.08965","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"},{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G245159946","display_name":null,"funder_award_id":"P30054","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2975891205","display_name":null,"funder_award_id":"DMS2111020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3240178331","display_name":null,"funder_award_id":"DOC 78","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3445814695","display_name":null,"funder_award_id":"DMS2111020","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3871119780","display_name":null,"funder_award_id":"P30054","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4700501153","display_name":null,"funder_award_id":"DOC 78","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W617206983","https://openalex.org/W647490872","https://openalex.org/W1564864701","https://openalex.org/W1967884132","https://openalex.org/W1968558958","https://openalex.org/W1991648154","https://openalex.org/W1999318406","https://openalex.org/W2017714771","https://openalex.org/W2018965660","https://openalex.org/W2020151808","https://openalex.org/W2022097729","https://openalex.org/W2022685032","https://openalex.org/W2022808639","https://openalex.org/W2025850615","https://openalex.org/W2032571282","https://openalex.org/W2041540906","https://openalex.org/W2044695655","https://openalex.org/W2047319386","https://openalex.org/W2052131944","https://openalex.org/W2069720235","https://openalex.org/W2079279226","https://openalex.org/W2117913366","https://openalex.org/W2134837756","https://openalex.org/W2137678186","https://openalex.org/W2524888845","https://openalex.org/W2805551240","https://openalex.org/W2936036145","https://openalex.org/W2962785898","https://openalex.org/W2963645054","https://openalex.org/W2964685603","https://openalex.org/W3006909054","https://openalex.org/W3099393693","https://openalex.org/W3102362377","https://openalex.org/W3106260400","https://openalex.org/W3126267920","https://openalex.org/W3132907149","https://openalex.org/W3157655418","https://openalex.org/W4236165936","https://openalex.org/W4292366025"],"related_works":["https://openalex.org/W3080507995","https://openalex.org/W2048060650","https://openalex.org/W3107612632","https://openalex.org/W3118397387","https://openalex.org/W3006082280","https://openalex.org/W3130104871","https://openalex.org/W2912767766","https://openalex.org/W3006067198","https://openalex.org/W2946024484","https://openalex.org/W3138184840","https://openalex.org/W2051216605","https://openalex.org/W3200687996","https://openalex.org/W1980291921","https://openalex.org/W2127650438","https://openalex.org/W2292453282","https://openalex.org/W1966029353","https://openalex.org/W3098082781","https://openalex.org/W3088369595","https://openalex.org/W2918770399","https://openalex.org/W2931033299"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,18,23,36,44,54,56,106,116,133],"attenuated":[4],"Westervelt":[5],"equation":[6,89],"in":[7,17,53,83],"pressure":[8],"formulation.":[9],"The":[10,41,93],"attenuation":[11],"is":[12,43,97],"by":[13,22],"various":[14],"models":[15],"proposed":[16],"literature":[19],"and":[20,136,141],"characterised":[21],"inclusion":[24],"of":[25,38,47,58,105,115],"non-local":[26,91],"operators":[27],"that":[28],"give":[29],"power":[30],"law":[31],"damping":[32],"as":[33],"opposed":[34],"to":[35,132],"exponential":[37],"classical":[39],"models.":[40],"goal":[42],"inverse":[45],"problem":[46],"recovering":[48],"a":[49,86,98,103],"spatially":[50],"dependent":[51],"coefficient":[52],"equation,":[55],"parameter":[57],"nonlinearity":[59],"<inline-formula":[60,120],"content-type=\"math/mathml\">":[61,121],"<mml:math":[62,122],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[63,123],"alttext=\"kappa":[64],"left-parenthesis":[65],"x":[66],"right-parenthesis\">":[67],"<mml:semantics>":[68,125],"<mml:mrow>":[69],"<mml:mi>\u03ba</mml:mi>":[70,126],"<mml:mo":[71,74],"stretchy=\"false\">(</mml:mo>":[72],"<mml:mi>x</mml:mi>":[73],"stretchy=\"false\">)</mml:mo>":[75],"</mml:mrow>":[76],"<mml:annotation":[77,127],"encoding=\"application/x-tex\">\\kappa":[78],"(x)</mml:annotation>":[79],"</mml:semantics>":[80,129],"</mml:math>":[81,130],"</inline-formula>,":[82],"what":[84],"becomes":[85],"nonlinear":[87],"hyperbolic":[88],"with":[90],"terms.":[92],"overposed":[94,134],"measured":[95],"data":[96,135],"time":[99],"trace":[100],"taken":[101],"on":[102],"subset":[104],"domain":[107],"or":[108],"its":[109,146],"boundary.":[110],"We":[111],"shall":[112],"show":[113],"injectivity":[114],"linearised":[117],"map":[118],"from":[119,137],"alttext=\"kappa\">":[124],"encoding=\"application/x-tex\">\\kappa</mml:annotation>":[128],"</inline-formula>":[131],"this":[138],"basis":[139],"develop":[140],"analyse":[142],"Newton-type":[143],"schemes":[144],"for":[145],"effective":[147],"recovery.":[148]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}