{"id":"https://openalex.org/W2132468176","doi":"https://doi.org/10.1137/15m1022367","title":"Reconstruction Procedures for Two Inverse Scattering Problems Without the Phase Information","display_name":"Reconstruction Procedures for Two Inverse Scattering Problems Without the Phase Information","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2132468176","doi":"https://doi.org/10.1137/15m1022367","mag":"2132468176"},"language":"en","primary_location":{"id":"doi:10.1137/15m1022367","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1022367","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5006099683","display_name":"Michael V. Klibanov","orcid":"https://orcid.org/0000-0001-5179-6879"},"institutions":[{"id":"https://openalex.org/I102149020","display_name":"University of North Carolina at Charlotte","ror":"https://ror.org/04dawnj30","country_code":"US","type":"education","lineage":["https://openalex.org/I102149020"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael V. Klibanov","raw_affiliation_strings":["University of North Carolina at Charlotte*"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of North Carolina at Charlotte*","institution_ids":["https://openalex.org/I102149020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091094738","display_name":"V. G. Romanov","orcid":"https://orcid.org/0000-0002-5426-4277"},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Vladimir G. Romanov","raw_affiliation_strings":["Novosibirsk state university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Novosibirsk state university","institution_ids":["https://openalex.org/I188973947"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":24.2123,"has_fulltext":false,"cited_by_count":89,"citation_normalized_percentile":{"value":0.99925936,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"76","issue":"1","first_page":"178","last_page":"196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9983999729156494,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9958000183105469,"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/inverse-problem","display_name":"Inverse problem","score":0.7569326162338257},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.753860592842102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6915242075920105},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5416529774665833},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5239189267158508},{"id":"https://openalex.org/keywords/inverse-scattering-transform","display_name":"Inverse scattering transform","score":0.4806146025657654},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.4583240747451782},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.414511114358902},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40508878231048584},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19536834955215454},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18627870082855225},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1358109712600708}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.7569326162338257},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.753860592842102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6915242075920105},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5416529774665833},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5239189267158508},{"id":"https://openalex.org/C136628613","wikidata":"https://www.wikidata.org/wiki/Q17098188","display_name":"Inverse scattering transform","level":4,"score":0.4806146025657654},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.4583240747451782},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.414511114358902},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40508878231048584},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19536834955215454},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18627870082855225},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1358109712600708},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1022367","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1022367","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1468538915","display_name":null,"funder_award_id":"W911NF-15-1-0233","funder_id":"https://openalex.org/F4320338295","funder_display_name":"Army Research Laboratory"},{"id":"https://openalex.org/G1841980472","display_name":null,"funder_award_id":"N00014-15-1-2330","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G6202710951","display_name":null,"funder_award_id":"14-01-00208","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G6713438582","display_name":null,"funder_award_id":"W911NF-15-1-0233","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"},{"id":"https://openalex.org/F4320338295","display_name":"Army Research Laboratory","ror":"https://ror.org/011hc8f90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W315631680","https://openalex.org/W361637455","https://openalex.org/W619564700","https://openalex.org/W621927936","https://openalex.org/W1510779360","https://openalex.org/W1517237161","https://openalex.org/W1521778258","https://openalex.org/W1523113578","https://openalex.org/W1555224164","https://openalex.org/W1866311589","https://openalex.org/W1965499806","https://openalex.org/W1982092780","https://openalex.org/W1983223664","https://openalex.org/W1996493475","https://openalex.org/W2001998908","https://openalex.org/W2002400157","https://openalex.org/W2016782326","https://openalex.org/W2017586161","https://openalex.org/W2017995052","https://openalex.org/W2018207223","https://openalex.org/W2019843291","https://openalex.org/W2021457366","https://openalex.org/W2022294513","https://openalex.org/W2028817727","https://openalex.org/W2039771789","https://openalex.org/W2041716445","https://openalex.org/W2058463209","https://openalex.org/W2058583833","https://openalex.org/W2064098737","https://openalex.org/W2064274523","https://openalex.org/W2064532740","https://openalex.org/W2080368551","https://openalex.org/W2082531160","https://openalex.org/W2084750801","https://openalex.org/W2084880047","https://openalex.org/W2097517979","https://openalex.org/W2117692113","https://openalex.org/W2120440916","https://openalex.org/W2126074755","https://openalex.org/W2170540013","https://openalex.org/W2323692108","https://openalex.org/W2520812953","https://openalex.org/W2591593131","https://openalex.org/W2962764176","https://openalex.org/W2963366171","https://openalex.org/W3104428006"],"related_works":["https://openalex.org/W2994306356","https://openalex.org/W2120820547","https://openalex.org/W4388295276","https://openalex.org/W2790147798","https://openalex.org/W4241983757","https://openalex.org/W143225781","https://openalex.org/W2520812953","https://openalex.org/W2071531878","https://openalex.org/W2037222243","https://openalex.org/W1975488373"],"abstract_inverted_index":{"This":[0],"is":[1,43,64,68,104,111,131,142],"a":[2,109,124,145],"continuation":[3],"of":[4,8,40,60,147,154],"two":[5],"recent":[6],"publications":[7],"the":[9,54,58,61,72,78,83,88,100,120,134,148,155],"authors":[10],"[J.":[11,46],"Inverse":[12,20,47],"Ill-Posed":[13,21,48],"Probl.,":[14,22,49],"23":[15,23,50],"(2015),":[16,24,51],"pp.":[17,25,52],"415--426;":[18],"J.":[19],"187--193]":[26],"about":[27],"reconstruction":[28,129,140],"procedures":[29],"for":[30,57,77],"three-dimensional":[31],"(3-D)":[32],"phaseless":[33,73],"inverse":[34,74,91,101,135],"scattering":[35,75],"problems.":[36],"The":[37,94,138],"main":[38],"novelty":[39],"this":[41],"paper":[42],"that,":[44],"unlike":[45],"187--193],":[53],"Born":[55],"approximation":[56],"case":[59],"wave-like":[62,80],"equation":[63,81],"not":[65],"considered.":[66],"It":[67],"shown":[69],"here":[70],"that":[71],"problem":[76,103,146],"3-D":[79],"in":[82],"frequency":[84],"domain":[85],"leads":[86],"to":[87,107],"well":[89],"known":[90],"kinematic":[92,102],"problem.":[93],"uniqueness":[95],"theorem":[96],"follows.":[97],"Still,":[98],"since":[99],"very":[105],"hard":[106],"solve,":[108],"linearization":[110],"applied.":[112],"More":[113],"precisely,":[114],"geodesic":[115],"lines":[116],"are":[117],"replaced":[118],"with":[119],"straight":[121],"lines.":[122],"As":[123],"result,":[125],"an":[126],"approximate":[127],"explicit":[128],"formula":[130],"obtained":[132],"via":[133,143],"Radon":[136],"transform.":[137],"second":[139],"method":[141],"solving":[144],"integral":[149,152],"geometry":[150],"using":[151],"equations":[153],"Abel":[156],"type.":[157]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
