{"id":"https://openalex.org/W1507713021","doi":"https://doi.org/10.23919/ecc.2003.7085271","title":"A regularization method for nonlinear inverse problems by using a Volterra model","display_name":"A regularization method for nonlinear inverse problems by using a Volterra model","publication_year":2003,"publication_date":"2003-09-01","ids":{"openalex":"https://openalex.org/W1507713021","doi":"https://doi.org/10.23919/ecc.2003.7085271","mag":"1507713021"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2003.7085271","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2003.7085271","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 European Control Conference (ECC)","raw_type":"proceedings-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/A5053160902","display_name":"G. Bibes","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210113334","https://openalex.org/I4210116740","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"G. Bibes","raw_affiliation_strings":["LAII, Laboratoire d'Automatique et d'Informatique Industrielle, Poitiers Cedex, France","Laboratoire d'Automatique et d'Informatique Industrielle, LAII-ESIP, 40 Avenue du recteur Pineau, 86022 Poitiers Cedex, France"],"affiliations":[{"raw_affiliation_string":"LAII, Laboratoire d'Automatique et d'Informatique Industrielle, Poitiers Cedex, France","institution_ids":["https://openalex.org/I4210116740"]},{"raw_affiliation_string":"Laboratoire d'Automatique et d'Informatique Industrielle, LAII-ESIP, 40 Avenue du recteur Pineau, 86022 Poitiers Cedex, France","institution_ids":["https://openalex.org/I4210116740"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108520369","display_name":"R\u00e9gis Ouvrard","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210113334","https://openalex.org/I4210116740","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R. Ouvrard","raw_affiliation_strings":["LAII, Laboratoire d'Automatique et d'Informatique Industrielle, Poitiers Cedex, France","Laboratoire d'Automatique et d'Informatique Industrielle, LAII-ESIP, 40 Avenue du recteur Pineau, 86022 Poitiers Cedex, France"],"affiliations":[{"raw_affiliation_string":"LAII, Laboratoire d'Automatique et d'Informatique Industrielle, Poitiers Cedex, France","institution_ids":["https://openalex.org/I4210116740"]},{"raw_affiliation_string":"Laboratoire d'Automatique et d'Informatique Industrielle, LAII-ESIP, 40 Avenue du recteur Pineau, 86022 Poitiers Cedex, France","institution_ids":["https://openalex.org/I4210116740"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055051320","display_name":"Patrick Coirault","orcid":"https://orcid.org/0000-0001-7359-5728"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210113334","https://openalex.org/I4210116740","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P. Coirault","raw_affiliation_strings":["LAII, Laboratoire d'Automatique et d'Informatique Industrielle, Poitiers Cedex, France","Laboratoire d'Automatique et d'Informatique Industrielle, LAII-ESIP, 40 Avenue du recteur Pineau, 86022 Poitiers Cedex, France"],"affiliations":[{"raw_affiliation_string":"LAII, Laboratoire d'Automatique et d'Informatique Industrielle, Poitiers Cedex, France","institution_ids":["https://openalex.org/I4210116740"]},{"raw_affiliation_string":"Laboratoire d'Automatique et d'Informatique Industrielle, LAII-ESIP, 40 Avenue du recteur Pineau, 86022 Poitiers Cedex, France","institution_ids":["https://openalex.org/I4210116740"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053160902"],"corresponding_institution_ids":["https://openalex.org/I4210116740"],"apc_list":null,"apc_paid":null,"fwci":1.0122,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69654394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"2068","last_page":"2072"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11236","display_name":"Control Systems and Identification","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11205","display_name":"Numerical methods in inverse problems","score":0.993399977684021,"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/orthonormal-basis","display_name":"Orthonormal basis","score":0.7621349096298218},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.7507883310317993},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6532435417175293},{"id":"https://openalex.org/keywords/volterra-series","display_name":"Volterra series","score":0.6474138498306274},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6386603116989136},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6310293674468994},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5805090665817261},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5552465915679932},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5541780591011047},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5516628623008728},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5100041627883911},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4860568344593048},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.42223289608955383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41677623987197876},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3167881369590759},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.19797345995903015},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1369328796863556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11125853657722473}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.7621349096298218},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.7507883310317993},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6532435417175293},{"id":"https://openalex.org/C2778532037","wikidata":"https://www.wikidata.org/wiki/Q3957891","display_name":"Volterra series","level":3,"score":0.6474138498306274},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6386603116989136},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6310293674468994},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5805090665817261},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5552465915679932},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5541780591011047},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5516628623008728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5100041627883911},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4860568344593048},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.42223289608955383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41677623987197876},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3167881369590759},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.19797345995903015},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1369328796863556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11125853657722473},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.23919/ecc.2003.7085271","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2003.7085271","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-03759402v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03759402","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc. European Control Conference (ECC 2003), Sep 2003, Cambridge,U.K., Unknown Region","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W389445767","https://openalex.org/W616910851","https://openalex.org/W1532863457","https://openalex.org/W1749484284","https://openalex.org/W1991777572","https://openalex.org/W1993291428","https://openalex.org/W2025902812","https://openalex.org/W2030211026","https://openalex.org/W2087070363","https://openalex.org/W2149846618","https://openalex.org/W2153944695"],"related_works":["https://openalex.org/W2749105521","https://openalex.org/W1971450333","https://openalex.org/W2360343897","https://openalex.org/W140737605","https://openalex.org/W2564453433","https://openalex.org/W3188213007","https://openalex.org/W2374214022","https://openalex.org/W1947575127","https://openalex.org/W2029137001","https://openalex.org/W376746440"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,21,30,39,82],"nonlinear":[4,40],"inverse":[5,37],"problem":[6],"is":[7,12,51,57],"proposed.":[8],"The":[9,24],"main":[10],"idea":[11],"to":[13,20,28,59,65],"apply":[14],"the":[15,61,67,70],"well":[16],"known":[17],"Tikhonov":[18],"regularization":[19],"Volterra":[22,25,71,79],"model.":[23],"model":[26,72],"allows":[27],"represent":[29],"large":[31],"variety":[32],"of":[33,77],"nonlinearities,":[34],"but":[35],"for":[36],"problem,":[38],"optimization":[41],"procedure":[42],"must":[43],"be":[44],"used":[45],"and":[46,64],"an":[47,75],"important":[48],"computational":[49,55,62],"burden":[50,63],"required.":[52],"A":[53],"particular":[54],"implementation":[56],"proposed":[58],"reduce":[60],"simplify":[66],"use.":[68],"Here":[69],"consists":[73],"in":[74],"approximation":[76],"each":[78],"kernel":[80],"by":[81],"multidimensional":[83],"orthonormal":[84],"basis":[85],"expansion.":[86]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
