{"id":"https://openalex.org/W2963541216","doi":"https://doi.org/10.1137/17m1142697","title":"A New Numerical Approach to Inverse Transport Equation with Error Analysis","display_name":"A New Numerical Approach to Inverse Transport Equation with Error Analysis","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2963541216","doi":"https://doi.org/10.1137/17m1142697","mag":"2963541216"},"language":"en","primary_location":{"id":"doi:10.1137/17m1142697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1142697","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical 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/A5100438891","display_name":"Qin Li","orcid":"https://orcid.org/0000-0001-9210-8948"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Qin Li","raw_affiliation_strings":["University of Wisconsin-Madison, #TAB#"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009937786","display_name":"Ruiwen Shu","orcid":"https://orcid.org/0000-0002-7269-7877"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ruiwen Shu","raw_affiliation_strings":["Univ. of Maryland,#TAB#"],"affiliations":[{"raw_affiliation_string":"Univ. of Maryland,#TAB#","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100335932","display_name":"Li Wang","orcid":"https://orcid.org/0000-0002-0593-8175"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100438891"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29847227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"56","issue":"6","first_page":"3358","last_page":"3385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.995199978351593,"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":0.995199978351593,"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/T12304","display_name":"Radiative Heat Transfer Studies","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.9783999919891357,"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/inverse-problem","display_name":"Inverse problem","score":0.6641128659248352},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6467306613922119},{"id":"https://openalex.org/keywords/radiative-transfer","display_name":"Radiative transfer","score":0.6323118209838867},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5597302913665771},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5572891235351562},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5095765590667725},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46508851647377014},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4436270296573639},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.43530598282814026},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.4130322337150574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26701754331588745},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10731780529022217},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.09114110469818115}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6641128659248352},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6467306613922119},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.6323118209838867},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5597302913665771},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5572891235351562},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5095765590667725},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46508851647377014},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4436270296573639},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.43530598282814026},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.4130322337150574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26701754331588745},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10731780529022217},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.09114110469818115},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1142697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1142697","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1971761822","https://openalex.org/W1985838959","https://openalex.org/W1996632146","https://openalex.org/W2005991120","https://openalex.org/W2006461826","https://openalex.org/W2006556102","https://openalex.org/W2011604718","https://openalex.org/W2016346232","https://openalex.org/W2022147895","https://openalex.org/W2024130663","https://openalex.org/W2033106066","https://openalex.org/W2046192310","https://openalex.org/W2051470240","https://openalex.org/W2062695418","https://openalex.org/W2072602259","https://openalex.org/W2074333289","https://openalex.org/W2088770471","https://openalex.org/W2134752347","https://openalex.org/W2138047631","https://openalex.org/W2143163067","https://openalex.org/W2257781909","https://openalex.org/W2286659138","https://openalex.org/W2318978041","https://openalex.org/W2412755389","https://openalex.org/W2591736287","https://openalex.org/W2765373598","https://openalex.org/W2962954762","https://openalex.org/W2963681985","https://openalex.org/W2977554044","https://openalex.org/W3099008000","https://openalex.org/W3101055543","https://openalex.org/W3102951105","https://openalex.org/W3106100609"],"related_works":["https://openalex.org/W2109418636","https://openalex.org/W2128608246","https://openalex.org/W2520812953","https://openalex.org/W2144075718","https://openalex.org/W3101167575","https://openalex.org/W2545426741","https://openalex.org/W1567523647","https://openalex.org/W4321641047","https://openalex.org/W2755915683","https://openalex.org/W2033816073"],"abstract_inverted_index":{"The":[0,59],"inverse":[1,46],"radiative":[2],"transfer":[3],"problem":[4,19,47,134],"finds":[5],"broad":[6],"applications":[7],"in":[8,66,188],"medical":[9],"imaging,":[10],"atmospheric":[11],"science,":[12],"astronomy,":[13],"and":[14,28,85,138,147,162,179],"many":[15],"other":[16],"areas.":[17],"This":[18],"intends":[20],"to":[21,43,63,90,111,143,186],"recover":[22,144],"optical":[23],"properties,":[24],"denoted":[25],"as":[26,48],"absorption":[27,146],"the":[29,33,45,53,56,78,83,86,102,113,122,125,132,145,156,159,163,172,176,182,189],"scattering":[30,148],"coefficient":[31],"of":[32,77,82,119,124,158],"media,":[34],"through":[35],"source-measurement":[36],"pairs.":[37],"A":[38],"typical":[39],"computational":[40],"approach":[41,109],"is":[42,61,74,88,110,184],"form":[44],"a":[49,97],"PDE-constraint":[50],"optimization,":[51,161],"with":[52,168],"minimizer":[54],"being":[55],"to-be-recovered":[57],"coefficients.":[58],"method":[60],"tested":[62],"be":[64,166],"efficient":[65],"practice,":[67],"but":[68],"it":[69],"lacks":[70],"analytical":[71],"justification:":[72],"there":[73],"no":[75],"guarantee":[76],"existence":[79],"or":[80],"uniqueness":[81],"minimizer,":[84],"error":[87,164,183],"hard":[89],"quantify.":[91],"In":[92,151,171],"this":[93,152],"paper,":[94],"we":[95,154,174],"provide":[96],"different":[98],"algorithm":[99],"by":[100],"levering":[101],"ideas":[103],"from":[104],"singular":[105],"decomposition":[106],"analysis.":[107],"Our":[108],"decompose":[112],"measurements":[114],"into":[115,135],"three":[116],"components,":[117],"two":[118,126,136,141],"which":[120],"encode":[121],"information":[123],"coefficients,":[127],"respectively.":[128],"We":[129],"then":[130],"split":[131],"optimization":[133],"subproblems":[137],"use":[139],"those":[140],"components":[142],"coefficients":[149],"separately.":[150],"regard,":[153],"prove":[155],"well-posedness":[157],"new":[160],"could":[165],"quantified":[167],"better":[169],"precision.":[170],"end,":[173],"incorporate":[175],"diffusive":[177,190],"scaling":[178],"show":[180],"that":[181],"harder":[185],"control":[187],"limit.":[191]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}