{"id":"https://openalex.org/W2911283415","doi":"https://doi.org/10.3390/jimaging5020027","title":"Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems","display_name":"Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems","publication_year":2019,"publication_date":"2019-02-08","ids":{"openalex":"https://openalex.org/W2911283415","doi":"https://doi.org/10.3390/jimaging5020027","mag":"2911283415","pmid":"https://pubmed.ncbi.nlm.nih.gov/34460475"},"language":"en","primary_location":{"id":"doi:10.3390/jimaging5020027","is_oa":true,"landing_page_url":"https://doi.org/10.3390/jimaging5020027","pdf_url":"https://www.mdpi.com/2313-433X/5/2/27/pdf?version=1550727958","source":{"id":"https://openalex.org/S2736465063","display_name":"Journal of Imaging","issn_l":"2313-433X","issn":["2313-433X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Imaging","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2313-433X/5/2/27/pdf?version=1550727958","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029344226","display_name":"Yu Zhong","orcid":"https://orcid.org/0000-0003-0209-4074"},"institutions":[{"id":"https://openalex.org/I115228651","display_name":"Agency for Science, Technology and Research","ror":"https://ror.org/036wvzt09","country_code":"SG","type":"government","lineage":["https://openalex.org/I115228651"]},{"id":"https://openalex.org/I3004594783","display_name":"Institute of High Performance Computing","ror":"https://ror.org/02n0ejh50","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3004594783","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Yu Zhong","raw_affiliation_strings":["Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore"],"raw_orcid":"https://orcid.org/0000-0003-0209-4074","affiliations":[{"raw_affiliation_string":"Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore","institution_ids":["https://openalex.org/I3004594783","https://openalex.org/I115228651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038032064","display_name":"Kuiwen Xu","orcid":"https://orcid.org/0000-0002-4943-5668"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kuiwen Xu","raw_affiliation_strings":["Key Lab of RF Circuits and Systems of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Lab of RF Circuits and Systems of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029344226"],"corresponding_institution_ids":["https://openalex.org/I115228651","https://openalex.org/I3004594783"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1732},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1732},"fwci":0.6975,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.66907253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"5","issue":"2","first_page":"27","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":1.0,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":1.0,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.7025412321090698},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.611674427986145},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.5963236093521118},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.583856463432312},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5831671953201294},{"id":"https://openalex.org/keywords/contraction-mapping","display_name":"Contraction mapping","score":0.5105682611465454},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.507103443145752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49839067459106445},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4533689022064209},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4424687623977661},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.4393632411956787},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4229414463043213},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41506487131118774},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3631972670555115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3604785203933716},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2992715537548065},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.18434569239616394},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.16513296961784363}],"concepts":[{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.7025412321090698},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.611674427986145},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.5963236093521118},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.583856463432312},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5831671953201294},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.5105682611465454},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.507103443145752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49839067459106445},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4533689022064209},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4424687623977661},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.4393632411956787},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4229414463043213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41506487131118774},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3631972670555115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3604785203933716},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2992715537548065},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.18434569239616394},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.16513296961784363},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/jimaging5020027","is_oa":true,"landing_page_url":"https://doi.org/10.3390/jimaging5020027","pdf_url":"https://www.mdpi.com/2313-433X/5/2/27/pdf?version=1550727958","source":{"id":"https://openalex.org/S2736465063","display_name":"Journal of Imaging","issn_l":"2313-433X","issn":["2313-433X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Imaging","raw_type":"journal-article"},{"id":"pmid:34460475","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34460475","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of imaging","raw_type":null},{"id":"pmh:oai:doaj.org/article:11a5eac0424d492e86c0710003e1c878","is_oa":false,"landing_page_url":"https://doaj.org/article/11a5eac0424d492e86c0710003e1c878","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Imaging, Vol 5, Iss 2, p 27 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2313-433X/5/2/27/","is_oa":true,"landing_page_url":"http://doi.org/10.3390/jimaging5020027","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Imaging","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8320915","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8320915","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Imaging","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/jimaging5020027","is_oa":true,"landing_page_url":"https://doi.org/10.3390/jimaging5020027","pdf_url":"https://www.mdpi.com/2313-433X/5/2/27/pdf?version=1550727958","source":{"id":"https://openalex.org/S2736465063","display_name":"Journal of Imaging","issn_l":"2313-433X","issn":["2313-433X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Imaging","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5199999809265137,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320324471","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2911283415.pdf","grobid_xml":"https://content.openalex.org/works/W2911283415.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W315413564","https://openalex.org/W1523113578","https://openalex.org/W1972054485","https://openalex.org/W1982072775","https://openalex.org/W1983322501","https://openalex.org/W1988597682","https://openalex.org/W2003147468","https://openalex.org/W2004251455","https://openalex.org/W2005305931","https://openalex.org/W2012096072","https://openalex.org/W2035489376","https://openalex.org/W2069118714","https://openalex.org/W2076202158","https://openalex.org/W2087077577","https://openalex.org/W2088841962","https://openalex.org/W2093334127","https://openalex.org/W2098579833","https://openalex.org/W2100632699","https://openalex.org/W2100737159","https://openalex.org/W2101422133","https://openalex.org/W2114284286","https://openalex.org/W2124087147","https://openalex.org/W2133034273","https://openalex.org/W2141760377","https://openalex.org/W2143368686","https://openalex.org/W2144559213","https://openalex.org/W2151959024","https://openalex.org/W2153307923","https://openalex.org/W2187410708","https://openalex.org/W2307575536","https://openalex.org/W2743348370","https://openalex.org/W2801403878","https://openalex.org/W6669534634","https://openalex.org/W6672602138","https://openalex.org/W6686897888"],"related_works":["https://openalex.org/W2375684291","https://openalex.org/W2354676191","https://openalex.org/W3188646203","https://openalex.org/W2909957174","https://openalex.org/W4246278799","https://openalex.org/W136674370","https://openalex.org/W2105527480","https://openalex.org/W2052387497","https://openalex.org/W2054809420","https://openalex.org/W2307575536"],"abstract_inverted_index":{"Inverse":[0],"scattering":[1,72],"problems":[2,128],"(ISPs)":[3],"stand":[4],"at":[5],"the":[6,39,45,68,70,75,79,82,89,108,112,115,125,143,146,154,157,172,178,182,188,192,201,204,211,231,241],"center":[7],"of":[8,27,114,141,145,191],"many":[9],"important":[10],"imaging":[11],"applications,":[12],"such":[13],"as":[14],"geophysical":[15],"explorations,":[16],"industrial":[17],"non-destructive":[18],"testing,":[19],"bio-medical":[20],"imaging,":[21],"etc.":[22],"Recently,":[23],"a":[24,55,59,64],"new":[25,56,105],"type":[26,117],"contraction":[28,65,212,217],"integral":[29,49],"equation":[30,50],"for":[31,78,107],"inversion":[32],"(CIE-I)":[33],"has":[34],"been":[35],"proposed":[36,193],"to":[37,102,163,209],"tackle":[38],"two-dimensional":[40],"electromagnetic":[41],"ISPs,":[42,83],"in":[43,81,87,221],"which":[44],"usually":[46,161],"employed":[47],"Lippmann-Schwinger":[48],"(LSIE)":[51],"is":[52,84,150,197],"transformed":[53],"into":[54],"form":[57],"with":[58,129,133,148,156,195,203],"modified":[60,90],"medium":[61],"contrast":[62,135,223],"via":[63],"mapping.":[66],"With":[67,111],"CIE-I,":[69],"multiple":[71],"effects,":[73],"i.e.,":[74,215],"physical":[76,94],"reason":[77],"nonlinearity":[80],"substantially":[85],"suppressed":[86],"estimating":[88],"contrast,":[91,226],"without":[92],"compromising":[93],"modeling.":[95],"In":[96,174],"this":[97,104],"paper,":[98],"we":[99,207,228],"firstly":[100],"propose":[101,208],"implement":[103],"CIE-I":[106,149,196],"three-dimensional":[109],"ISPs.":[110],"help":[113],"FFT":[116],"twofold":[118],"subspace-based":[119],"optimization":[120],"method":[121,194],"(TSOM),":[122],"when":[123,176],"handling":[124,177],"highly":[126],"nonlinear":[127],"strong":[130],"scatterers,":[131],"those":[132],"higher":[134],"and/or":[136],"larger":[137],"dimensions":[138],"(in":[139],"terms":[140],"wavelengths),":[142],"performance":[144],"inversions":[147,160],"much":[151,198],"better":[152],"than":[153,200],"ones":[155],"LSIE,":[158],"wherein":[159],"converge":[162],"local":[164],"minima":[165],"that":[166,230],"may":[167],"be":[168,234],"far":[169],"away":[170],"from":[171],"solution.":[173],"addition,":[175],"moderate":[179],"scatterers":[180],"(those":[181],"LSIE":[183],"modeling":[184],"can":[185,233],"still":[186],"handle),":[187],"convergence":[189,232],"speed":[190],"faster":[199],"one":[202],"LSIE.":[205],"Secondly,":[206],"relax":[210],"mapping":[213],"condition,":[214],"different":[216],"mappings":[218],"are":[219],"used":[220],"updating":[222],"sources":[224],"and":[225,227],"find":[229],"further":[235],"accelerated.":[236],"Several":[237],"numerical":[238],"tests":[239],"illustrate":[240],"aforementioned":[242],"interests.":[243]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}