{"id":"https://openalex.org/W2140626180","doi":"https://doi.org/10.1137/130938657","title":"Numerical Implementation of Geodesic X-Ray Transforms and Their Inversion","display_name":"Numerical Implementation of Geodesic X-Ray Transforms and Their Inversion","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2140626180","doi":"https://doi.org/10.1137/130938657","mag":"2140626180"},"language":"en","primary_location":{"id":"doi:10.1137/130938657","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130938657","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1309.6042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024080388","display_name":"Fran\u00e7ois Monard","orcid":"https://orcid.org/0000-0003-2913-7644"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Monard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024080388"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4046,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73197908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","issue":"2","first_page":"1335","last_page":"1357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9829999804496765,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9775999784469604,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.8535946011543274},{"id":"https://openalex.org/keywords/solenoidal-vector-field","display_name":"Solenoidal vector field","score":0.8418217301368713},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.737267017364502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4911787211894989},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.42909106612205505},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.42859748005867004},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4243004024028778},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39801883697509766},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.33384567499160767},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30362290143966675},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.164341002702713}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.8535946011543274},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.8418217301368713},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.737267017364502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4911787211894989},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.42909106612205505},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42859748005867004},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4243004024028778},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39801883697509766},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33384567499160767},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30362290143966675},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.164341002702713},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130938657","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130938657","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"},{"id":"pmh:oai:arXiv.org:1309.6042","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1309.6042","pdf_url":"https://arxiv.org/pdf/1309.6042","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2140626180","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1309.6042v2","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.1309.6042","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1309.6042","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1309.6042","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1309.6042","pdf_url":"https://arxiv.org/pdf/1309.6042","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8616295710","display_name":"CMG COLLABORATIVE RESEARCH: Nonlinear elastic-wave inverse scattering and tomography- from cracks to mantle convection","funder_award_id":"1025372","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2140626180.pdf","grobid_xml":"https://content.openalex.org/works/W2140626180.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1586142979","https://openalex.org/W1622096124","https://openalex.org/W1949248870","https://openalex.org/W1970552792","https://openalex.org/W1975849239","https://openalex.org/W1985838959","https://openalex.org/W1987093744","https://openalex.org/W2001454270","https://openalex.org/W2003496107","https://openalex.org/W2010091409","https://openalex.org/W2033733331","https://openalex.org/W2047408599","https://openalex.org/W2052143526","https://openalex.org/W2056987756","https://openalex.org/W2058583833","https://openalex.org/W2074863718","https://openalex.org/W2156316288","https://openalex.org/W2280758432","https://openalex.org/W2314429677","https://openalex.org/W2950593275","https://openalex.org/W2951288821","https://openalex.org/W2951531770","https://openalex.org/W2963221109"],"related_works":["https://openalex.org/W2964339643","https://openalex.org/W2963587538","https://openalex.org/W2964268565","https://openalex.org/W1574468672","https://openalex.org/W2099327136","https://openalex.org/W3199135298","https://openalex.org/W2152394501","https://openalex.org/W3018620080","https://openalex.org/W2045444089","https://openalex.org/W2107488863","https://openalex.org/W1661363091","https://openalex.org/W2998588166","https://openalex.org/W89453633","https://openalex.org/W1752714314","https://openalex.org/W2110314207","https://openalex.org/W3157099481","https://openalex.org/W2902585561","https://openalex.org/W2566144401","https://openalex.org/W2963483244","https://openalex.org/W2396137871"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2],"numerical":[3,66],"implementation":[4],"of":[5,59,85],"the":[6,57,86],"geodesic":[7],"ray":[8],"transform":[9],"and":[10,15,32,61,74,83],"its":[11],"inversion":[12,26],"over":[13],"functions":[14],"solenoidal":[16],"vector":[17],"fields":[18],"on":[19],"two-dimensional":[20],"Riemannian":[21],"manifolds.":[22],"For":[23],"each":[24],"problem,":[25],"formulas":[27],"previously":[28],"derived":[29],"by":[30,44],"Pestov":[31],"Uhlmann":[33],"[Internat.":[34],"Math.":[35],"Res.":[36],"Notices,":[37],"80":[38],"(2004),":[39],"pp.":[40,52],"4331--4347]":[41],"then":[42],"extended":[43],"Krishnan":[45],"[J.":[46],"Inv.":[47],"Ill-Posed":[48],"Probl.,":[49],"18":[50],"(2010),":[51],"401--408]":[53],"are":[54,68,91],"implemented":[55],"in":[56],"case":[58],"simple":[60],"some":[62],"nonsimple":[63,78],"metrics.":[64],"These":[65],"tools":[67],"also":[69],"used":[70],"to":[71],"better":[72],"understand":[73],"gain":[75],"intuition":[76],"about":[77],"manifolds,":[79],"for":[80],"which":[81],"injectivity":[82],"stability":[84],"corresponding":[87],"integral":[88],"geometric":[89],"problems":[90],"still":[92],"under":[93],"active":[94],"study.":[95]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-07T08:38:57.713557","created_date":"2025-10-10T00:00:00"}