{"id":"https://openalex.org/W1989997740","doi":"https://doi.org/10.1137/s0036141001392785","title":"Recovery of Small Inhomogeneities from the Scattering Amplitude at a Fixed Frequency","display_name":"Recovery of Small Inhomogeneities from the Scattering Amplitude at a Fixed Frequency","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1989997740","doi":"https://doi.org/10.1137/s0036141001392785","mag":"1989997740"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141001392785","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001392785","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical 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/A5041497235","display_name":"Habib Ammari","orcid":"https://orcid.org/0000-0001-7278-4877"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Habib Ammari","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109035342","display_name":"\u0415\u043a\u0430\u0442\u0435\u0440\u0438\u043d\u0430 \u042f\u043a\u043e\u0432\u043b\u0435\u0432\u0430","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ekaterina Iakovleva","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085751232","display_name":"Shari Moskow","orcid":"https://orcid.org/0000-0002-8240-7247"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shari Moskow","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4428,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.87695777,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"34","issue":"4","first_page":"882","last_page":"900"},"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":0.9987999796867371,"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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7432282567024231},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6903183460235596},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.6837795972824097},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.6733964085578918},{"id":"https://openalex.org/keywords/scattering-amplitude","display_name":"Scattering amplitude","score":0.613254189491272},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5544984936714172},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.5192359089851379},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.49590882658958435},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.47683992981910706},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.43513065576553345},{"id":"https://openalex.org/keywords/scattering-theory","display_name":"Scattering theory","score":0.4299040138721466},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3666386902332306},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2731139063835144},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.22664353251457214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20207175612449646}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7432282567024231},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6903183460235596},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.6837795972824097},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.6733964085578918},{"id":"https://openalex.org/C153013531","wikidata":"https://www.wikidata.org/wiki/Q1322810","display_name":"Scattering amplitude","level":3,"score":0.613254189491272},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5544984936714172},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.5192359089851379},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.49590882658958435},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.47683992981910706},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.43513065576553345},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.4299040138721466},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3666386902332306},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2731139063835144},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.22664353251457214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20207175612449646}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036141001392785","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001392785","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W13927686","https://openalex.org/W51795062","https://openalex.org/W177010616","https://openalex.org/W177735991","https://openalex.org/W1523113578","https://openalex.org/W1965386465","https://openalex.org/W1969600843","https://openalex.org/W1971765522","https://openalex.org/W1979646278","https://openalex.org/W1982938970","https://openalex.org/W1992503250","https://openalex.org/W2013269090","https://openalex.org/W2018207223","https://openalex.org/W2049176462","https://openalex.org/W2062024414","https://openalex.org/W2063310370","https://openalex.org/W2084782137","https://openalex.org/W2086044352","https://openalex.org/W2101299564","https://openalex.org/W2125687349","https://openalex.org/W2155374487","https://openalex.org/W2505262635","https://openalex.org/W4232035096","https://openalex.org/W4237529375","https://openalex.org/W4255272544","https://openalex.org/W4285719527","https://openalex.org/W4297575314"],"related_works":["https://openalex.org/W2116581862","https://openalex.org/W629824820","https://openalex.org/W4246558539","https://openalex.org/W3151493211","https://openalex.org/W2886182558","https://openalex.org/W3100169344","https://openalex.org/W1525777291","https://openalex.org/W2078987483","https://openalex.org/W2979977619","https://openalex.org/W2158231092"],"abstract_inverted_index":{"We":[0,28],"rigorously":[1],"derive":[2],"the":[3,8,12,35,39,45,48,69],"leading":[4],"order":[5],"term":[6],"in":[7],"asymptotic":[9,32],"expansion":[10],"of":[11,15,18,22,25,37,44,47,71],"scattering":[13,52],"amplitude":[14,53],"a":[16,19,56],"collection":[17],"finite":[20],"number":[21],"dielectric":[23],"inhomogeneities":[24,50],"small":[26,49],"diameter.":[27],"then":[29],"apply":[30],"this":[31,65],"formula":[33],"for":[34],"purpose":[36],"identifying":[38],"location":[40],"and":[41],"certain":[42],"properties":[43],"shapes":[46],"from":[51],"measurements":[54],"at":[55],"fixed":[57],"frequency.":[58],"Our":[59],"main":[60],"idea":[61],"is":[62],"to":[63,68],"reduce":[64],"reconstruction":[66],"problem":[67],"calculation":[70],"an":[72],"inverse":[73],"Fourier":[74],"transform.":[75]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
