{"id":"https://openalex.org/W4221151305","doi":"https://doi.org/10.1137/21m1437810","title":"Imaging Anisotropic Conductivities from Current Densities","display_name":"Imaging Anisotropic Conductivities from Current Densities","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W4221151305","doi":"https://doi.org/10.1137/21m1437810"},"language":"en","primary_location":{"id":"doi:10.1137/21m1437810","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1437810","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://discovery.ucl.ac.uk/10153241/1/21m1437810.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023277730","display_name":"Huan Liu","orcid":"https://orcid.org/0000-0002-2217-0591"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I4210166603","display_name":"Jinling Institute of Technology","ror":"https://ror.org/05em1gq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166603"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Huan Liu","raw_affiliation_strings":["\\ddagger Department of Computer Science, University College London, London, WC1E 6BT, UK","\\dagger College of Science, Jinling Institute of Technology, Nanjing 211169, People's Republic of China","\\S School of Mathematics and Statistics, Wuhan University, and Hubei Key Laboratory of Computational Science (Wuhan University), Wuhan 430072, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\ddagger Department of Computer Science, University College London, London, WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"\\dagger College of Science, Jinling Institute of Technology, Nanjing 211169, People's Republic of China","institution_ids":["https://openalex.org/I4210166603"]},{"raw_affiliation_string":"\\S School of Mathematics and Statistics, Wuhan University, and Hubei Key Laboratory of Computational Science (Wuhan University), Wuhan 430072, People's Republic of China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039605463","display_name":"Bangti Jin","orcid":"https://orcid.org/0000-0002-3775-9155"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I4210166603","display_name":"Jinling Institute of Technology","ror":"https://ror.org/05em1gq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166603"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Bangti Jin","raw_affiliation_strings":["\\S School of Mathematics and Statistics, Wuhan University, and Hubei Key Laboratory of Computational Science (Wuhan University), Wuhan 430072, People's Republic of China","\\dagger College of Science, Jinling Institute of Technology, Nanjing 211169, People's Republic of China","\\ddagger Department of Computer Science, University College London, London, WC1E 6BT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\S School of Mathematics and Statistics, Wuhan University, and Hubei Key Laboratory of Computational Science (Wuhan University), Wuhan 430072, People's Republic of China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"\\dagger College of Science, Jinling Institute of Technology, Nanjing 211169, People's Republic of China","institution_ids":["https://openalex.org/I4210166603"]},{"raw_affiliation_string":"\\ddagger Department of Computer Science, University College London, London, WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055337142","display_name":"Xiliang Lu","orcid":"https://orcid.org/0000-0002-7592-5994"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I4210166603","display_name":"Jinling Institute of Technology","ror":"https://ror.org/05em1gq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166603"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Xiliang Lu","raw_affiliation_strings":["\\S School of Mathematics and Statistics, Wuhan University, and Hubei Key Laboratory of Computational Science (Wuhan University), Wuhan 430072, People's Republic of China","\\dagger College of Science, Jinling Institute of Technology, Nanjing 211169, People's Republic of China","\\ddagger Department of Computer Science, University College London, London, WC1E 6BT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\S School of Mathematics and Statistics, Wuhan University, and Hubei Key Laboratory of Computational Science (Wuhan University), Wuhan 430072, People's Republic of China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"\\dagger College of Science, Jinling Institute of Technology, Nanjing 211169, People's Republic of China","institution_ids":["https://openalex.org/I4210166603"]},{"raw_affiliation_string":"\\ddagger Department of Computer Science, University College London, London, WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2232,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.42690615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"2","first_page":"860","last_page":"891"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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":0.9977999925613403,"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/T10572","display_name":"Geophysical and Geoelectrical Methods","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8022091388702393},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.725411057472229},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.545016348361969},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5243813395500183},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5031394362449646},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4956279993057251},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46911337971687317},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4672871232032776},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.46254202723503113},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4159987270832062},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24736052751541138},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.125206857919693}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8022091388702393},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.725411057472229},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.545016348361969},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5243813395500183},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5031394362449646},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4956279993057251},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46911337971687317},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4672871232032776},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.46254202723503113},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4159987270832062},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24736052751541138},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.125206857919693},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1437810","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1437810","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:eprints.ucl.ac.uk.OAI2:10153241","is_oa":true,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/10153241/","pdf_url":"https://discovery.ucl.ac.uk/10153241/1/21m1437810.pdf","source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Imaging Sciences , 15 (2) pp. 860-891. (2022)","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:10153241","is_oa":true,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/10153241/","pdf_url":"https://discovery.ucl.ac.uk/10153241/1/21m1437810.pdf","source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Imaging Sciences , 15 (2) pp. 860-891. (2022)","raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2343787110","display_name":"Stochastic iterative regularization: theory, algorithms and applications","funder_award_id":"EP/T000864/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2543385244","display_name":null,"funder_award_id":"EP/T000864/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5928362628","display_name":null,"funder_award_id":"12101276","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6266162256","display_name":null,"funder_award_id":"2020YFA0714200","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7063149761","display_name":null,"funder_award_id":"11871385","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7249912578","display_name":null,"funder_award_id":"2020YFA0714200","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7858055918","display_name":null,"funder_award_id":"jit-fhxm-202117","funder_id":"https://openalex.org/F4320327505","funder_display_name":"Jinling Institute of Technology"},{"id":"https://openalex.org/G8198834040","display_name":null,"funder_award_id":"040521200103","funder_id":"https://openalex.org/F4320327505","funder_display_name":"Jinling Institute of Technology"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327505","display_name":"Jinling Institute of Technology","ror":"https://ror.org/05em1gq62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221151305.pdf"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W568417546","https://openalex.org/W1570089119","https://openalex.org/W1593155044","https://openalex.org/W1977948239","https://openalex.org/W1978393821","https://openalex.org/W1980386319","https://openalex.org/W1984583900","https://openalex.org/W1986264877","https://openalex.org/W1996926091","https://openalex.org/W2003491112","https://openalex.org/W2004324765","https://openalex.org/W2006519579","https://openalex.org/W2007548249","https://openalex.org/W2010554795","https://openalex.org/W2013916391","https://openalex.org/W2027568813","https://openalex.org/W2046465662","https://openalex.org/W2049784481","https://openalex.org/W2050971853","https://openalex.org/W2053482768","https://openalex.org/W2059078751","https://openalex.org/W2063623344","https://openalex.org/W2070280570","https://openalex.org/W2076929784","https://openalex.org/W2079187543","https://openalex.org/W2082187902","https://openalex.org/W2082949320","https://openalex.org/W2084742835","https://openalex.org/W2091360472","https://openalex.org/W2141952290","https://openalex.org/W2168832646","https://openalex.org/W2170382756","https://openalex.org/W2278879664","https://openalex.org/W2321310861","https://openalex.org/W2471307131","https://openalex.org/W2506849756","https://openalex.org/W2566817631","https://openalex.org/W2761020868","https://openalex.org/W2767279209","https://openalex.org/W2949737535","https://openalex.org/W2952619184","https://openalex.org/W2962927629","https://openalex.org/W2964312073","https://openalex.org/W3100172662","https://openalex.org/W3100193126","https://openalex.org/W3100938728","https://openalex.org/W3101047122","https://openalex.org/W3102084676","https://openalex.org/W3102921918","https://openalex.org/W3104604322","https://openalex.org/W3195230178","https://openalex.org/W3204708751","https://openalex.org/W4210300254","https://openalex.org/W4231675611"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W2006251942","https://openalex.org/W4327738859","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613"],"abstract_inverted_index":{"In":[0,120],"this":[1],"paper,":[2],"we":[3,92,122],"propose":[4],"and":[5,60,79],"analyze":[6],"a":[7,17,22,35,94,124],"reconstruction":[8],"algorithm":[9,127],"for":[10,128],"imaging":[11],"an":[12],"anisotropic":[13],"conductivity":[14,70],"tensor":[15,71],"in":[16,72],"second-order":[18],"elliptic":[19],"PDE":[20],"with":[21,40,66,108],"nonzero":[23],"Dirichlet":[24],"boundary":[25],"condition":[26],"from":[27],"internal":[28],"current":[29],"densities.":[30],"It":[31],"is":[32,46],"based":[33],"on":[34],"regularized":[36,84],"output":[37],"least-squares":[38],"formulation":[39,85],"the":[41,50,58,63,69,73,75,83,87,98,102,105,111,115,130,142,145],"standard":[42,51],"$L^2(\\Omega)^{d,d}$":[43],"penalty,":[44],"which":[45],"then":[47],"discretized":[48,99],"by":[49],"Galerkin":[52],"finite":[53],"element":[54],"method.":[55,147],"We":[56,134],"establish":[57],"continuity":[59],"differentiability":[61],"of":[62,77,82,89,97,104,118,144],"forward":[64],"map":[65],"respect":[67,109],"to":[68,110,140],"$L^p(\\Omega)^{d,d}$-norms,":[74],"existence":[76],"minimizers":[78],"optimality":[80,132],"systems":[81],"using":[86,114],"concept":[88],"H-convergence.":[90,119],"Further,":[91],"provide":[93],"detailed":[95],"analysis":[96],"problem,":[100],"especially":[101],"convergence":[103],"discrete":[106,116],"approximations":[107],"mesh":[112],"size,":[113],"counterpart":[117],"addition,":[121],"develop":[123],"projected":[125],"Newton":[126],"solving":[129],"first-order":[131],"system.":[133],"present":[135],"extensive":[136],"two-dimensional":[137],"numerical":[138],"examples":[139],"show":[141],"efficiency":[143],"proposed":[146]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}