{"id":"https://openalex.org/W3201449912","doi":"https://doi.org/10.3390/sym13091702","title":"Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media","display_name":"Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media","publication_year":2021,"publication_date":"2021-09-15","ids":{"openalex":"https://openalex.org/W3201449912","doi":"https://doi.org/10.3390/sym13091702","mag":"3201449912"},"language":"en","primary_location":{"id":"doi:10.3390/sym13091702","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091702","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1702/pdf?version=1631854745","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/9/1702/pdf?version=1631854745","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058352766","display_name":"A. Carpio","orcid":"https://orcid.org/0000-0001-8623-6521"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ana Carpio","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Facultad de Matem\u00e1ticas, Universidad Complutense de Madrid, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8623-6521","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Facultad de Matem\u00e1ticas, Universidad Complutense de Madrid, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050524181","display_name":"Mar\u00eda-Luisa Rap\u00fan","orcid":"https://orcid.org/0000-0001-5787-5252"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Mar\u00eda-Luisa Rap\u00fan","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada a la Ingenier\u00eda Aeroespacial, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0001-5787-5252","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada a la Ingenier\u00eda Aeroespacial, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050524181"],"corresponding_institution_ids":["https://openalex.org/I88060688"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8908,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71452703,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"13","issue":"9","first_page":"1702","last_page":"1702"},"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":0.9879000186920166,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9829999804496765,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.6157735586166382},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6103960871696472},{"id":"https://openalex.org/keywords/attenuation","display_name":"Attenuation","score":0.5912837982177734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5244460701942444},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4830532670021057},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4591997563838959},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.41297537088394165},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.39959678053855896},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32969218492507935},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2628185749053955},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.23848766088485718},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22820842266082764},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18770655989646912},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14538413286209106},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11469918489456177}],"concepts":[{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.6157735586166382},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6103960871696472},{"id":"https://openalex.org/C184652730","wikidata":"https://www.wikidata.org/wiki/Q2357982","display_name":"Attenuation","level":2,"score":0.5912837982177734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5244460701942444},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4830532670021057},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4591997563838959},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.41297537088394165},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.39959678053855896},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32969218492507935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2628185749053955},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.23848766088485718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22820842266082764},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18770655989646912},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14538413286209106},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11469918489456177}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym13091702","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091702","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1702/pdf?version=1631854745","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:www.ucm.es:74953","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.ucm.es/id/eprint/74953/1/carpio_multifrequency.pdf","source":{"id":"https://openalex.org/S4306400298","display_name":"Library Open Repository (Universidad Complutense Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I121748325","host_organization_name":"Universidad Complutense de Madrid","host_organization_lineage":["https://openalex.org/I121748325"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:4f7ba0c23557465f9569f797073d313e","is_oa":true,"landing_page_url":"https://doaj.org/article/4f7ba0c23557465f9569f797073d313e","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 9, p 1702 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/9/1702/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13091702","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13091702","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091702","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1702/pdf?version=1631854745","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G3112477053","display_name":null,"funder_award_id":"PID2020-112796RB-C21","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5338095294","display_name":null,"funder_award_id":"PID2020-114173RB-I00.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8525811521","display_name":null,"funder_award_id":"MTM2017-84446-C2-1-R","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3201449912.pdf"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W1503613404","https://openalex.org/W1509515451","https://openalex.org/W1517670975","https://openalex.org/W1970536458","https://openalex.org/W1972054485","https://openalex.org/W1986924342","https://openalex.org/W1994133356","https://openalex.org/W1995067704","https://openalex.org/W2001979313","https://openalex.org/W2009020532","https://openalex.org/W2013565263","https://openalex.org/W2014148782","https://openalex.org/W2027068534","https://openalex.org/W2036941264","https://openalex.org/W2037677143","https://openalex.org/W2039545154","https://openalex.org/W2041741421","https://openalex.org/W2043822820","https://openalex.org/W2046155034","https://openalex.org/W2046536612","https://openalex.org/W2046943221","https://openalex.org/W2054782886","https://openalex.org/W2057396386","https://openalex.org/W2059621702","https://openalex.org/W2061502567","https://openalex.org/W2062481980","https://openalex.org/W2076508235","https://openalex.org/W2077344911","https://openalex.org/W2079009605","https://openalex.org/W2080292934","https://openalex.org/W2087400951","https://openalex.org/W2089378574","https://openalex.org/W2090894265","https://openalex.org/W2108174537","https://openalex.org/W2115181480","https://openalex.org/W2134222132","https://openalex.org/W2144634920","https://openalex.org/W2157700312","https://openalex.org/W2158202781","https://openalex.org/W2169880671","https://openalex.org/W2200158341","https://openalex.org/W2236884385","https://openalex.org/W2434575905","https://openalex.org/W2478917285","https://openalex.org/W2507502634","https://openalex.org/W2580765095","https://openalex.org/W2745778491","https://openalex.org/W2898623945","https://openalex.org/W2906994872","https://openalex.org/W2924846246","https://openalex.org/W2950106307","https://openalex.org/W2950886526","https://openalex.org/W2957416722","https://openalex.org/W2991574319","https://openalex.org/W3008476977","https://openalex.org/W3008929414","https://openalex.org/W3012730131","https://openalex.org/W3034165978","https://openalex.org/W3102179962","https://openalex.org/W3105642946","https://openalex.org/W3198072405","https://openalex.org/W4250458689","https://openalex.org/W4293183906","https://openalex.org/W6646467628","https://openalex.org/W6653741131","https://openalex.org/W6690053583"],"related_works":["https://openalex.org/W2128608246","https://openalex.org/W2520812953","https://openalex.org/W3101167575","https://openalex.org/W1567523647","https://openalex.org/W4321641047","https://openalex.org/W2755915683","https://openalex.org/W2331917905","https://openalex.org/W2144075718","https://openalex.org/W2033816073","https://openalex.org/W2545426741"],"abstract_inverted_index":{"Detecting":[0],"objects":[1,28,67,102],"hidden":[2],"in":[3,34,53,104,125,142],"a":[4,61,94,143],"medium":[5],"is":[6],"an":[7],"inverse":[8,73],"problem.":[9],"Given":[10],"data":[11,33,85],"recorded":[12,84],"at":[13],"detectors":[14],"when":[15],"sources":[16],"emit":[17],"waves":[18,52],"that":[19,29],"interact":[20],"with":[21,107],"the":[22,35,38,43,48,51,54,65,72,79,83,113,126,134,155,170],"medium,":[23],"we":[24,92],"aim":[25],"to":[26,100,122],"find":[27],"would":[30],"generate":[31],"similar":[32],"presence":[36,55],"of":[37,50,56,71,133,151,177],"same":[39],"waves.":[40],"In":[41,89],"opposition,":[42],"associated":[44],"forward":[45,80],"problem":[46],"describes":[47],"evolution":[49],"known":[57],"objects.":[58],"This":[59],"gives":[60],"symmetry":[62],"relation:":[63],"if":[64],"true":[66],"(the":[68],"desired":[69],"solution":[70],"problem)":[74],"were":[75],"considered":[76],"for":[77,174],"solving":[78],"problem,":[81],"then":[82],"should":[86],"be":[87,120],"returned.":[88],"this":[90],"paper,":[91],"develop":[93],"topological":[95],"derivative-based":[96],"multifrequency":[97],"iterative":[98],"algorithm":[99,135],"reconstruct":[101],"buried":[103,159],"attenuating":[105],"media":[106],"limited":[108],"aperture":[109],"data.":[110],"We":[111,146],"demonstrate":[112],"method":[114],"on":[115,169],"half-space":[116],"configurations,":[117],"which":[118,139],"can":[119,147],"related":[121],"problems":[123],"set":[124],"whole":[127],"space":[128],"by":[129],"symmetry.":[130],"One-step":[131],"implementations":[132],"provide":[136],"initial":[137],"approximations,":[138],"are":[140],"improved":[141],"few":[144],"iterations.":[145],"locate":[148],"object":[149,166],"components":[150],"sizes":[152],"smaller":[153],"than":[154],"main":[156],"components,":[157],"or":[158],"deeper":[160],"inside.":[161],"However,":[162],"attenuation":[163],"effects":[164],"hinder":[165],"detection":[167],"depending":[168],"size":[171],"and":[172],"depth":[173],"fixed":[175],"ranges":[176],"frequencies.":[178]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
