{"id":"https://openalex.org/W3036080769","doi":"https://doi.org/10.1137/20m1386955","title":"Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem","display_name":"Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3036080769","doi":"https://doi.org/10.1137/20m1386955","mag":"3036080769"},"language":"en","primary_location":{"id":"doi:10.1137/20m1386955","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1386955","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.12299","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085726540","display_name":"Houcine Meftahi","orcid":"https://orcid.org/0000-0001-5524-9370"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Houcine Meftahi","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5524-9370","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085726540"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05898927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"53","issue":"6","first_page":"6326","last_page":"6354"},"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.998199999332428,"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/T10977","display_name":"Optical Imaging and Spectroscopy Techniques","score":0.9932000041007996,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7849695682525635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.741277813911438},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6721780896186829},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6286369562149048},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5070252418518066},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46310847997665405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45643818378448486},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4424096941947937},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4403592646121979}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7849695682525635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741277813911438},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6721780896186829},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6286369562149048},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5070252418518066},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46310847997665405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45643818378448486},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4424096941947937},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4403592646121979},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1386955","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1386955","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"},{"id":"pmh:oai:arXiv.org:2006.12299","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.12299","pdf_url":"https://arxiv.org/pdf/2006.12299","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":null,"raw_type":"text"},{"id":"mag:3036080769","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.12299.pdf","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.2006.12299","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.12299","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:2006.12299","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.12299","pdf_url":"https://arxiv.org/pdf/2006.12299","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3036080769.pdf","grobid_xml":"https://content.openalex.org/works/W3036080769.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W1970300524","https://openalex.org/W1972581758","https://openalex.org/W1976225084","https://openalex.org/W1979860790","https://openalex.org/W1980889189","https://openalex.org/W1981696101","https://openalex.org/W1988978892","https://openalex.org/W1989942411","https://openalex.org/W1991117271","https://openalex.org/W2002178240","https://openalex.org/W2003209827","https://openalex.org/W2010057327","https://openalex.org/W2018207223","https://openalex.org/W2022220775","https://openalex.org/W2031629416","https://openalex.org/W2032246197","https://openalex.org/W2033106066","https://openalex.org/W2034712897","https://openalex.org/W2036661666","https://openalex.org/W2046465662","https://openalex.org/W2049176462","https://openalex.org/W2050559599","https://openalex.org/W2052797733","https://openalex.org/W2053972348","https://openalex.org/W2063073969","https://openalex.org/W2065585720","https://openalex.org/W2065658257","https://openalex.org/W2069009977","https://openalex.org/W2072090418","https://openalex.org/W2073494671","https://openalex.org/W2085102456","https://openalex.org/W2095463076","https://openalex.org/W2112538771","https://openalex.org/W2123224804","https://openalex.org/W2153207045","https://openalex.org/W2158959733","https://openalex.org/W2164668388","https://openalex.org/W2169935136","https://openalex.org/W2247675853","https://openalex.org/W2320454589","https://openalex.org/W2557648131","https://openalex.org/W2593150298","https://openalex.org/W2598715715","https://openalex.org/W2625102685","https://openalex.org/W2744028846","https://openalex.org/W2747659684","https://openalex.org/W2789008732","https://openalex.org/W2789946195","https://openalex.org/W2792557313","https://openalex.org/W2886699879","https://openalex.org/W2887950507","https://openalex.org/W2948654209","https://openalex.org/W2994896604","https://openalex.org/W3100470565","https://openalex.org/W3100841790","https://openalex.org/W3101532053","https://openalex.org/W3102523415","https://openalex.org/W3102759745","https://openalex.org/W3104405385","https://openalex.org/W4237848465"],"related_works":["https://openalex.org/W3102759745","https://openalex.org/W1992132227","https://openalex.org/W2899838972","https://openalex.org/W2949990229","https://openalex.org/W154314707","https://openalex.org/W2041608360","https://openalex.org/W3040912106","https://openalex.org/W3025120101","https://openalex.org/W3153514035","https://openalex.org/W2097801150","https://openalex.org/W2556375120","https://openalex.org/W1974379802","https://openalex.org/W2724737791","https://openalex.org/W2284451488","https://openalex.org/W2024192553","https://openalex.org/W3045693162","https://openalex.org/W3153978601","https://openalex.org/W2111939340","https://openalex.org/W1991137391","https://openalex.org/W2095542106"],"abstract_inverted_index":{"In":[0,58],"this":[1,135],"paper,":[2],"we":[3,45,94,157],"consider":[4],"the":[5,21,35,40,61,83,91,115,119,126,131],"inverse":[6,92],"problem":[7,19,117],"of":[8,54,85,103,114,134,147],"recovering":[9],"a":[10,27,47,65,70,78,96,101,153],"diffusion":[11,41,55],"and":[12,30,56,137],"absorption":[13,36],"coefficients":[14],"in":[15],"steady-state":[16],"optical":[17],"tomography":[18],"from":[20],"Neumann-to-Dirichlet":[22],"map.":[23],"We":[24],"first":[25],"prove":[26,46],"Global":[28],"uniqueness":[29],"Lipschitz":[31,48],"stability":[32,49],"estimate":[33],"for":[34,51],"parameter":[37],"provided":[38],"that":[39],"is":[42,142],"known.":[43],"Then,":[44],"result":[50,80],"simultaneous":[52],"recovery":[53],"absorption.":[57],"both":[59],"cases":[60],"parameters":[62,105],"belong":[63],"to":[64,107,124],"known":[66,72],"finite":[67],"subspace":[68],"with":[69,82],"priori":[71],"bounds.":[73],"The":[74,112,140],"proofs":[75],"relies":[76],"on":[77,152],"monotonicity":[79],"combined":[81],"techniques":[84],"localized":[86],"potentials.":[87],"To":[88],"numerically":[89],"solve":[90],"problem,":[93],"propose":[95],"Kohn-Vogeliustype":[97],"cost":[98],"functional":[99],"over":[100],"class":[102],"admissible":[104],"subject":[106],"two":[108],"boundary":[109],"value":[110],"problems.":[111],"reformulation":[113],"minimization":[116],"via":[118],"Neumann-toDirichlet":[120],"operator":[121,136],"allows":[122],"us":[123],"obtain":[125],"optimality":[127],"conditions":[128],"by":[129,145],"using":[130],"Frechet":[132],"differentiability":[133],"its":[138],"inverse.":[139],"reconstruction":[141],"then":[143],"performed":[144],"means":[146],"an":[148],"iterative":[149],"algorithm":[150],"based":[151],"quasi-Newton":[154],"method.":[155],"Finally,":[156],"illustrate":[158],"some":[159],"numerical":[160],"results.":[161]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
