{"id":"https://openalex.org/W330923118","doi":"https://doi.org/10.1137/15m1016412","title":"Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces","display_name":"Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W330923118","doi":"https://doi.org/10.1137/15m1016412","mag":"330923118"},"language":"en","primary_location":{"id":"doi:10.1137/15m1016412","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1016412","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5024080388","display_name":"Fran\u00e7ois Monard","orcid":"https://orcid.org/0000-0003-2913-7644"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Monard","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024080388"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":5.0441,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.95022536,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"48","issue":"2","first_page":"1155","last_page":"1177"},"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9822999835014343,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8102412223815918},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.8025782108306885},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6199955940246582},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5867730379104614},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.53431236743927},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5323323011398315},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.5291717052459717},{"id":"https://openalex.org/keywords/holomorphic-function","display_name":"Holomorphic function","score":0.464324414730072},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4246349632740021},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25660526752471924}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8102412223815918},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.8025782108306885},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6199955940246582},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5867730379104614},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.53431236743927},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5323323011398315},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5291717052459717},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.464324414730072},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4246349632740021},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25660526752471924},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1016412","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1016412","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3469843115","display_name":"Coupled-physics imaging methods and geodesic X-ray transforms","funder_award_id":"1514820","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8288337460","display_name":"Inverse Boundary Problems","funder_award_id":"1265958","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W101849871","https://openalex.org/W284076903","https://openalex.org/W1580413560","https://openalex.org/W1586142979","https://openalex.org/W1590193249","https://openalex.org/W1802177642","https://openalex.org/W1970552792","https://openalex.org/W1974106862","https://openalex.org/W1982840759","https://openalex.org/W1987018660","https://openalex.org/W1988029467","https://openalex.org/W1993230286","https://openalex.org/W2012566185","https://openalex.org/W2016713499","https://openalex.org/W2019498616","https://openalex.org/W2024456949","https://openalex.org/W2030727075","https://openalex.org/W2034933793","https://openalex.org/W2044040194","https://openalex.org/W2045444089","https://openalex.org/W2073378807","https://openalex.org/W2111991040","https://openalex.org/W2126829454","https://openalex.org/W2156316288","https://openalex.org/W2160354518","https://openalex.org/W2170475474","https://openalex.org/W2280758432","https://openalex.org/W2314429677","https://openalex.org/W2908224753","https://openalex.org/W2962703662","https://openalex.org/W2962993693","https://openalex.org/W2963162295","https://openalex.org/W2963221109","https://openalex.org/W2964339643","https://openalex.org/W3098698687","https://openalex.org/W3105384701","https://openalex.org/W3139752542"],"related_works":["https://openalex.org/W2211201902","https://openalex.org/W3094515845","https://openalex.org/W2982338311","https://openalex.org/W4386732633","https://openalex.org/W4237698157","https://openalex.org/W4248353673","https://openalex.org/W2295512640","https://openalex.org/W2089223129","https://openalex.org/W2952868792","https://openalex.org/W3099176754"],"abstract_inverted_index":{"We":[0],"derive":[1],"explicit":[2,37],"reconstruction":[3,61],"formulas":[4,32],"for":[5,43],"the":[6,15,69,80,84,87,90,121,124],"attenuated":[7],"geodesic":[8],"X-ray":[9],"transform":[10],"over":[11],"functions":[12,63],"and,":[13],"in":[14,47,56,66,79,100],"case":[16],"of":[17,25,62,83,123,131],"nonvanishing":[18],"attenuation,":[19],"vector":[20],"fields,":[21],"on":[22,35],"a":[23,57,128],"class":[24],"simple":[26,132],"Riemannian":[27],"surfaces":[28,133],"with":[29],"boundary.":[30],"These":[31],"partly":[33],"rely":[34],"new":[36],"approaches":[38],"to":[39,127],"construct":[40],"continuous":[41],"right-inverses":[42,92],"backprojection":[44],"operators":[45],"(and,":[46],"turn,":[48],"holomorphic":[49],"integrating":[50],"factors),":[51],"which":[52],"were":[53],"previously":[54],"unavailable":[55],"systematic":[58],"form.":[59],"The":[60],"is":[64],"presented":[65],"two":[67],"ways,":[68],"latter":[70],"being":[71],"motivated":[72],"by":[73],"numerical":[74],"considerations":[75],"and":[76,103],"successfully":[77],"implemented":[78],"last":[81,118],"section":[82],"paper":[85],"(before":[86],"appendix).":[88],"Constructing":[89],"aforementioned":[91],"requires":[93],"that":[94],"certain":[95],"Fredholm":[96],"equations,":[97],"first":[98],"appearing":[99],"[L.":[101],"Pestov":[102],"G.":[104],"Uhlmann,":[105],"Int.":[106],"Math.":[107],"Res.":[108],"Not.,":[109],"2004":[110],"(2004),":[111],"pp.":[112],"4331--4347],":[113],"be":[114],"invertible.":[115],"Whether":[116],"this":[117],"condition":[119],"reduces":[120],"applicability":[122],"overall":[125],"approach":[126],"strict":[129],"subset":[130],"remains":[134],"open":[135],"at":[136],"present.":[137]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}