{"id":"https://openalex.org/W2758271156","doi":"https://doi.org/10.1137/17m1149699","title":"Uniqueness in Inverse Scattering Problems with Phaseless Far-Field Data at a Fixed Frequency","display_name":"Uniqueness in Inverse Scattering Problems with Phaseless Far-Field Data at a Fixed Frequency","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2758271156","doi":"https://doi.org/10.1137/17m1149699","mag":"2758271156"},"language":"en","primary_location":{"id":"doi:10.1137/17m1149699","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1149699","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/A5067196344","display_name":"Xiaoxu Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoxu Xu","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences,","University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences,","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100335192","display_name":"Bo Zhang","orcid":"https://orcid.org/0000-0001-7355-0941"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210095018","display_name":"National Center for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/00s97k668","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210095018"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Zhang","raw_affiliation_strings":["NCMIS, LSEC and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China and School of Mathematical Sciences,","University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NCMIS, LSEC and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China and School of Mathematical Sciences,","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210095018","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047634561","display_name":"Haiwen Zhang","orcid":"https://orcid.org/0000-0003-4035-4754"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiwen Zhang","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":"https://orcid.org/0000-0003-4035-4754","affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.4642,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.9883,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"78","issue":"3","first_page":"1737","last_page":"1753"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9998000264167786,"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":0.9983999729156494,"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/mathematics","display_name":"Mathematics","score":0.5866995453834534},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5762490630149841},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.5547924637794495},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5489509701728821},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5157577991485596},{"id":"https://openalex.org/keywords/near-and-far-field","display_name":"Near and far field","score":0.4803713262081146},{"id":"https://openalex.org/keywords/plane-wave","display_name":"Plane wave","score":0.44569188356399536},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.4386943280696869},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4156007468700409},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.41174179315567017},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3980867266654968},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3044825792312622},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17902931571006775},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1627333164215088},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15160328149795532},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.110362708568573}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5866995453834534},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5762490630149841},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.5547924637794495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5489509701728821},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5157577991485596},{"id":"https://openalex.org/C25227671","wikidata":"https://www.wikidata.org/wiki/Q13405516","display_name":"Near and far field","level":2,"score":0.4803713262081146},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.44569188356399536},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.4386943280696869},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4156007468700409},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.41174179315567017},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3980867266654968},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3044825792312622},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17902931571006775},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1627333164215088},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15160328149795532},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.110362708568573}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1149699","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1149699","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/G2772607984","display_name":"\u969c\u788d\u4e0e\u4ecb\u8d28\u6df7\u5408\u53cd\u6563\u5c04\u95ee\u9898\u7684\u6570\u5b66\u7406\u8bba\u548c\u6570\u503c\u7b97\u6cd5","funder_award_id":"11571355","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G465819471","display_name":null,"funder_award_id":"61379093","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4969315547","display_name":null,"funder_award_id":"91630309","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G503881559","display_name":null,"funder_award_id":"11501558","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6238626454","display_name":null,"funder_award_id":"91430102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320336876","display_name":"National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences","ror":"https://ror.org/00s97k668"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W614932401","https://openalex.org/W1523113578","https://openalex.org/W1964510609","https://openalex.org/W1971231406","https://openalex.org/W1983223664","https://openalex.org/W1994926960","https://openalex.org/W2003659905","https://openalex.org/W2009766219","https://openalex.org/W2021457366","https://openalex.org/W2028817727","https://openalex.org/W2030764277","https://openalex.org/W2031445862","https://openalex.org/W2039771789","https://openalex.org/W2058717368","https://openalex.org/W2059427263","https://openalex.org/W2078397124","https://openalex.org/W2082531160","https://openalex.org/W2089337236","https://openalex.org/W2091027394","https://openalex.org/W2132259582","https://openalex.org/W2132468176","https://openalex.org/W2136436000","https://openalex.org/W2137278936","https://openalex.org/W2139369096","https://openalex.org/W2142949395","https://openalex.org/W2166262861","https://openalex.org/W2215705268","https://openalex.org/W2332783578","https://openalex.org/W2416067360","https://openalex.org/W2500401920","https://openalex.org/W2509331849","https://openalex.org/W2512673524","https://openalex.org/W2515007495","https://openalex.org/W2535155561","https://openalex.org/W2538725373","https://openalex.org/W2597150118","https://openalex.org/W2607200862","https://openalex.org/W2741129808","https://openalex.org/W2963366171","https://openalex.org/W2963829305","https://openalex.org/W2964056273","https://openalex.org/W3098670860","https://openalex.org/W3098877181","https://openalex.org/W3101123351","https://openalex.org/W3105593508"],"related_works":["https://openalex.org/W2109418636","https://openalex.org/W2128608246","https://openalex.org/W2520812953","https://openalex.org/W3101167575","https://openalex.org/W2545426741","https://openalex.org/W1567523647","https://openalex.org/W4321641047","https://openalex.org/W2755915683","https://openalex.org/W2144075718","https://openalex.org/W2033816073"],"abstract_inverted_index":{"This":[0],"paper":[1,223],"is":[2,24,140,162,189,218],"concerned":[3],"with":[4,10,127,197],"uniqueness":[5,192],"in":[6,172,194,221],"inverse":[7,195],"acoustic":[8],"scattering":[9,196],"phaseless":[11,65,113,198],"far-field":[12,35,66,114,199,215,230],"data":[13],"at":[14,86,130],"a":[15,87,131,141,146,226],"fixed":[16,88,132],"frequency.":[17,89],"The":[18],"main":[19],"difficulty":[20],"of":[21,30,33,63,76,78,101,103,121,123,155,158,175,185,209,213,228],"this":[22,91,188,222],"problem":[23],"the":[25,31,34,43,59,64,83,96,99,112,135,138,153,159,173,183,190,207,210,214,229],"so-called":[26],"translation":[27,60],"invariance":[28,61],"property":[29,62],"modulus":[32],"pattern":[36,67],"generated":[37,116],"by":[38,71,111,117,224],"one":[39],"plane":[40,80,125],"wave":[41],"as":[42,82],"incident":[44,84],"field.":[45],"Based":[46],"on":[47,206],"our":[48,186],"previous":[49],"work":[50],"[":[51],"J.":[52],"Comput.":[53],"Phys.,":[54],"345":[55],"(2017),":[56],"pp.":[57],"58--73],":[58],"can":[68,107],"be":[69,108,145],"broken":[70],"using":[72,225],"infinitely":[73,118],"many":[74,119],"sets":[75,120],"superpositions":[77,122],"two":[79,124],"waves":[81,126],"fields":[85],"In":[90],"paper,":[92],"we":[93],"prove":[94],"that":[95,137,166],"obstacle":[97,139,151],"and":[98,152,164],"index":[100,154],"refraction":[102,156],"an":[104],"inhomogeneous":[105,160],"medium":[106,161],"uniquely":[109],"determined":[110],"patterns":[115],"different":[128],"directions":[129],"frequency":[133],"under":[134],"condition":[136],"priori":[142],"known":[143],"to":[144],"sound-soft":[147],"or":[148,170],"nonabsorbing":[149],"impedance":[150],"$n$":[157],"real-valued":[163],"satisfies":[165],"either":[167],"$n-1\\ge":[168],"c_1$":[169],"$n-1\\le-c_1$":[171],"support":[174],"$n-1$":[176],"for":[177],"some":[178],"positive":[179],"constant":[180],"$c_1$.":[181],"To":[182],"best":[184],"knowledge,":[187],"first":[191],"result":[193],"data.":[200],"Our":[201],"proofs":[202],"are":[203],"based":[204],"essentially":[205],"limit":[208],"normalized":[211],"eigenvalues":[212],"operators,":[216],"which":[217],"also":[219],"established":[220],"factorization":[227],"operators.":[231]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":5}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}
