{"id":"https://openalex.org/W1980619755","doi":"https://doi.org/10.1137/100786770","title":"Tomographic Reconstruction of the Curl and Divergence of 2D Vector Fields Taking Refractions into Account","display_name":"Tomographic Reconstruction of the Curl and Divergence of 2D Vector Fields Taking Refractions into Account","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1980619755","doi":"https://doi.org/10.1137/100786770","mag":"1980619755"},"language":"en","primary_location":{"id":"doi:10.1137/100786770","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786770","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057035548","display_name":"T. Pfitzenreiter","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tim Pfitzenreiter","raw_affiliation_strings":["tim.pfitzenreiter@hsu-hh.de#TAB#"],"affiliations":[{"raw_affiliation_string":"tim.pfitzenreiter@hsu-hh.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083589911","display_name":"Thomas Schuster","orcid":"https://orcid.org/0000-0002-2667-8691"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Schuster","raw_affiliation_strings":["thomas.schuster@uni-oldenburg.de#TAB#"],"affiliations":[{"raw_affiliation_string":"thomas.schuster@uni-oldenburg.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057035548"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2893,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.74024969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"4","issue":"1","first_page":"40","last_page":"56"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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":1.0,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.8373156785964966},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.6916183829307556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5559117794036865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5528770685195923},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5343968272209167},{"id":"https://openalex.org/keywords/radon-transform","display_name":"Radon transform","score":0.5067155957221985},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.45559123158454895},{"id":"https://openalex.org/keywords/refraction","display_name":"Refraction","score":0.43862012028694153},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3729000687599182},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34350645542144775},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.25395694375038147},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17039242386817932}],"concepts":[{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.8373156785964966},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6916183829307556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5559117794036865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5528770685195923},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5343968272209167},{"id":"https://openalex.org/C197231052","wikidata":"https://www.wikidata.org/wiki/Q979829","display_name":"Radon transform","level":2,"score":0.5067155957221985},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.45559123158454895},{"id":"https://openalex.org/C205318122","wikidata":"https://www.wikidata.org/wiki/Q72277","display_name":"Refraction","level":2,"score":0.43862012028694153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3729000687599182},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34350645542144775},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.25395694375038147},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17039242386817932},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100786770","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786770","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W645918899","https://openalex.org/W651883043","https://openalex.org/W1253232274","https://openalex.org/W1600485280","https://openalex.org/W1666853924","https://openalex.org/W1975849239","https://openalex.org/W1977506423","https://openalex.org/W1984036124","https://openalex.org/W1999383731","https://openalex.org/W2001490481","https://openalex.org/W2030815520","https://openalex.org/W2045646280","https://openalex.org/W2061782497","https://openalex.org/W2096632054","https://openalex.org/W2126829454","https://openalex.org/W2160354518","https://openalex.org/W2169835892","https://openalex.org/W2324461723","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2478780871","https://openalex.org/W1216769707","https://openalex.org/W3168011518","https://openalex.org/W4366307899","https://openalex.org/W2092258800","https://openalex.org/W2168649520","https://openalex.org/W2013135861","https://openalex.org/W2083529992","https://openalex.org/W1977506423","https://openalex.org/W2025438663"],"abstract_inverted_index":{"This":[0,154],"article":[1,155],"is":[2,44,74,81,91,100],"concerned":[3],"with":[4,76,102,157,181],"the":[5,9,23,26,38,41,50,62,67,77,103,111,115,127,142,147,163,175],"problem":[6],"of":[7,13,25,40,69,146,169],"reconstructing":[8],"curl":[10,143],"and":[11,114,144,172],"divergence":[12,145],"two-dimensional":[14],"(2D)":[15],"vector":[16,35,88,148],"fields":[17],"from":[18,126],"ultrasound":[19,28,42,63],"time-of-flight":[20],"measurements":[21],"taking":[22],"refraction":[24,39],"emitted":[27],"rays":[29],"into":[30],"account.":[31],"Usually,":[32],"in":[33,97],"2D":[34],"field":[36,149],"tomography":[37],"signal":[43,51,64],"neglected;":[45],"i.e.,":[46],"one":[47,164],"assumes":[48],"that":[49,61,73,99,183],"propagates":[52,65],"along":[53,66,118,187],"straight":[54,188],"lines.":[55,189],"We":[56,106],"address":[57],"refractive":[58,78],"effects,":[59],"assuming":[60],"geodesics":[68],"a":[70,95,108,123,166,185],"Riemannian":[71],"metric":[72],"associated":[75],"index":[79],"which":[80,121],"due":[82],"to":[83],"Fermat's":[84],"principle.":[85],"The":[86],"investigated":[87],"field,":[89],"however,":[90],"still":[92],"defined":[93],"on":[94,131,162,174],"domain":[96],"$\\mathbb{R}^2$":[98],"equipped":[101],"Euclidean":[104,128],"metric.":[105],"show":[107],"connection":[109],"between":[110],"ray":[112],"transforms":[113],"Radon":[116],"transform":[117],"geodesic":[119],"curves":[120],"generalizes":[122],"well-known":[124],"result":[125],"case.":[129],"Relying":[130],"this":[132],"relation,":[133],"we":[134],"develop":[135],"an":[136,178],"asymptotic":[137],"reconstruction":[138],"formula":[139],"for":[140],"computing":[141],"using":[150],"Fourier":[151],"integral":[152],"operators.":[153],"concludes":[156],"detailed":[158],"numerical":[159],"tests":[160],"proving":[161],"hand":[165,177],"good":[167],"performance":[168],"our":[170],"method":[171],"showing":[173],"other":[176],"improvement":[179],"compared":[180],"computations":[182],"assume":[184],"propagation":[186]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}