{"id":"https://openalex.org/W2020406985","doi":"https://doi.org/10.1137/06066970x","title":"The Quasi-Reversibility Method for Thermoacoustic Tomography in a Heterogeneous Medium","display_name":"The Quasi-Reversibility Method for Thermoacoustic Tomography in a Heterogeneous Medium","publication_year":2007,"publication_date":"2007-11-07","ids":{"openalex":"https://openalex.org/W2020406985","doi":"https://doi.org/10.1137/06066970x","mag":"2020406985"},"language":"en","primary_location":{"id":"doi:10.1137/06066970x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066970x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5011665383","display_name":"Christian Clason","orcid":"https://orcid.org/0000-0002-9948-8426"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christian Clason","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006099683","display_name":"Michael V. Klibanov","orcid":"https://orcid.org/0000-0001-5179-6879"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael V. Klibanov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011665383"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0425,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.93421244,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"30","issue":"1","first_page":"1","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"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/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.7866050004959106},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6734983325004578},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5909156799316406},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.567405104637146},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5330010652542114},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.5072855353355408},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4985637664794922},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49030664563179016},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.4887409210205078},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46098360419273376},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4608646631240845},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.44409361481666565},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.4263472557067871},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.4227929711341858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7866050004959106},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6734983325004578},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5909156799316406},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.567405104637146},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5330010652542114},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.5072855353355408},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4985637664794922},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49030664563179016},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.4887409210205078},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46098360419273376},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4608646631240845},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.44409361481666565},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.4263472557067871},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.4227929711341858},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/06066970x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06066970x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W115282090","https://openalex.org/W379254235","https://openalex.org/W592740744","https://openalex.org/W640847489","https://openalex.org/W968983006","https://openalex.org/W1505881492","https://openalex.org/W1532154335","https://openalex.org/W1570089119","https://openalex.org/W1968767220","https://openalex.org/W1976391307","https://openalex.org/W1991359259","https://openalex.org/W2011695259","https://openalex.org/W2014208632","https://openalex.org/W2018207223","https://openalex.org/W2022337355","https://openalex.org/W2025029279","https://openalex.org/W2030668043","https://openalex.org/W2032246197","https://openalex.org/W2033287169","https://openalex.org/W2033440212","https://openalex.org/W2036661666","https://openalex.org/W2038929555","https://openalex.org/W2040568794","https://openalex.org/W2042725413","https://openalex.org/W2048561965","https://openalex.org/W2053439426","https://openalex.org/W2073572636","https://openalex.org/W2073922020","https://openalex.org/W2084364352","https://openalex.org/W2090344516","https://openalex.org/W2094929691","https://openalex.org/W2122432836","https://openalex.org/W2129778820","https://openalex.org/W2133834935","https://openalex.org/W2147354348","https://openalex.org/W2149542824","https://openalex.org/W2162870748","https://openalex.org/W2168669828","https://openalex.org/W2170922253","https://openalex.org/W2566785243","https://openalex.org/W3021722416","https://openalex.org/W3140377161","https://openalex.org/W3194374079"],"related_works":["https://openalex.org/W2152537629","https://openalex.org/W2902113171","https://openalex.org/W1976964087","https://openalex.org/W3037639584","https://openalex.org/W4234788860","https://openalex.org/W2286968803","https://openalex.org/W2362811170","https://openalex.org/W4381378370","https://openalex.org/W4292134160","https://openalex.org/W2354909503"],"abstract_inverted_index":{"In":[0],"this":[1,75,140],"paper":[2],"we":[3,127,132],"consider":[4],"thermoacoustic":[5],"tomography":[6],"as":[7],"the":[8,17,37,46,50,91,98,114,117,137,143],"inverse":[9],"problem":[10,30,53,60,76,119],"of":[11,39,48,74,90,116,139,145],"determining":[12],"from":[13,94,148],"lateral":[14],"Cauchy":[15],"data":[16],"unknown":[18],"initial":[19,146],"conditions":[20,147],"in":[21,33,36],"a":[22,57,62,70,82,105,110,121],"wave":[23,99],"equation":[24],"with":[25,56],"spatially":[26],"varying":[27],"coefficients.":[28],"This":[29],"also":[31],"occurs":[32],"several":[34],"applications":[35],"area":[38],"medical":[40],"imaging":[41],"and":[42,77,88,150],"nondestructive":[43],"testing.":[44],"Using":[45],"method":[47,141],"quasi-reversibility,":[49],"original":[51],"ill-posed":[52],"is":[54,81],"replaced":[55],"boundary":[58,152],"value":[59],"for":[61,97,113,125,142],"fourth":[63],"order":[64],"partial":[65],"differential":[66],"equation.":[67],"We":[68,108],"find":[69],"weak":[71],"$H^2$":[72],"solution":[73,115],"show":[78],"that":[79],"it":[80],"well-posed":[83],"elliptic":[84],"problem.":[85],"Error":[86],"estimates":[87,96],"convergence":[89],"approximation":[92],"follow":[93],"observability":[95],"equation,":[100],"which":[101,126],"are":[102],"proved":[103],"using":[104],"Carleman":[106],"estimate.":[107],"derive":[109],"numerical":[111,134],"scheme":[112],"quasi-reversibility":[118],"by":[120],"B-spline":[122],"Galerkin":[123],"method,":[124],"give":[128],"error":[129],"estimates.":[130],"Finally,":[131],"present":[133],"results":[135],"supporting":[136],"robustness":[138],"reconstruction":[144],"full":[149],"limited":[151],"data.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
