{"id":"https://openalex.org/W2009765585","doi":"https://doi.org/10.1162/neco.2007.10-06-376","title":"A Cooperative Recurrent Neural Network for Solving <i>L</i><sub>1</sub> Estimation Problems with General Linear Constraints","display_name":"A Cooperative Recurrent Neural Network for Solving <i>L</i><sub>1</sub> Estimation Problems with General Linear Constraints","publication_year":2007,"publication_date":"2007-11-28","ids":{"openalex":"https://openalex.org/W2009765585","doi":"https://doi.org/10.1162/neco.2007.10-06-376","mag":"2009765585","pmid":"https://pubmed.ncbi.nlm.nih.gov/18370841"},"language":"en","primary_location":{"id":"doi:10.1162/neco.2007.10-06-376","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2007.10-06-376","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5113682730","display_name":"Youshen Xia","orcid":null},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Youshen Xia","raw_affiliation_strings":["College of Mathematics and Computer Science, Fuzhou University, China","College of Mathematics and Computer Science, Fuzhou University, China.ysxia2001@yahoo.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, Fuzhou University, China","institution_ids":["https://openalex.org/I80947539"]},{"raw_affiliation_string":"College of Mathematics and Computer Science, Fuzhou University, China.ysxia2001@yahoo.com","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039318050","display_name":"Mohamed S. Kamel","orcid":"https://orcid.org/0000-0001-6173-8082"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mohamed S. Kamel","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Waterloo, Canada","Department of Electrical and Computer Engineering, University of Waterloo, Canada.mkamel@pami.uwaterloo.ca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Waterloo, Canada.mkamel@pami.uwaterloo.ca","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3483,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.92644988,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"3","first_page":"844","last_page":"872"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6498685479164124},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5979050397872925},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5542890429496765},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.48812922835350037},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.47635698318481445},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.4733163118362427},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.4492253363132477},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38064607977867126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34926068782806396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33933210372924805},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2439941167831421}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6498685479164124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5979050397872925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5542890429496765},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.48812922835350037},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.47635698318481445},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.4733163118362427},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.4492253363132477},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38064607977867126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34926068782806396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33933210372924805},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2439941167831421},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008432","descriptor_name":"Mathematical Computing","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008432","descriptor_name":"Mathematical Computing","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008432","descriptor_name":"Mathematical Computing","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D011340","descriptor_name":"Problem Solving","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016014","descriptor_name":"Linear Models","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016477","descriptor_name":"Artifacts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016477","descriptor_name":"Artifacts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016477","descriptor_name":"Artifacts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1162/neco.2007.10-06-376","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2007.10-06-376","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:18370841","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18370841","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W39785869","https://openalex.org/W116303816","https://openalex.org/W1485391971","https://openalex.org/W1492221128","https://openalex.org/W1516681311","https://openalex.org/W1562895369","https://openalex.org/W2011903764","https://openalex.org/W2018503235","https://openalex.org/W2020960975","https://openalex.org/W2027504452","https://openalex.org/W2030563088","https://openalex.org/W2034619845","https://openalex.org/W2041465020","https://openalex.org/W2045528845","https://openalex.org/W2066776472","https://openalex.org/W2097521973","https://openalex.org/W2100129785","https://openalex.org/W2102555533","https://openalex.org/W2103855222","https://openalex.org/W2106390255","https://openalex.org/W2117182821","https://openalex.org/W2118204568","https://openalex.org/W2125191947","https://openalex.org/W2132687755","https://openalex.org/W2136208307","https://openalex.org/W2137161313","https://openalex.org/W2140426615","https://openalex.org/W2140499889","https://openalex.org/W2141106960","https://openalex.org/W2146694719","https://openalex.org/W2162406405","https://openalex.org/W2178935672","https://openalex.org/W2752885492","https://openalex.org/W2787523326","https://openalex.org/W3145128584"],"related_works":["https://openalex.org/W2372940580","https://openalex.org/W2101113459","https://openalex.org/W4225394202","https://openalex.org/W4298287631","https://openalex.org/W2953061907","https://openalex.org/W3032952384","https://openalex.org/W3034302643","https://openalex.org/W1847088711","https://openalex.org/W3036642985","https://openalex.org/W2187706389"],"abstract_inverted_index":{"The":[0,39],"constrained":[1,72,87],"L(1)":[2,12,32,73,88,126],"estimation":[3,13,33,74,89,127],"is":[4,51,94],"an":[5],"attractive":[6],"alternative":[7],"to":[8,96,99],"both":[9],"the":[10,15,60,86,91,100,113,125,136],"unconstrained":[11,70],"and":[14,50,71,121],"least":[16],"square":[17],"estimation.":[18],"In":[19],"this":[20],"letter,":[21],"we":[22],"propose":[23],"a":[24,57,117],"cooperative":[25],"recurrent":[26],"neural":[27,46,66,79],"network":[28,47],"(CRNN)":[29],"for":[30,53,68,84],"solving":[31,69,85],"problems":[34],"with":[35,81,109,124,129],"general":[36],"linear":[37],"constraints.":[38],"proposed":[40,61,92,114,137],"CRNN":[41,62,93,115,138],"model":[42],"combines":[43],"four":[44],"individual":[45],"models":[48],"automatically":[49],"suitable":[52],"parallel":[54],"implementation.":[55],"As":[56],"special":[58],"case,":[59],"includes":[63],"two":[64],"existing":[65,78,146],"networks":[67],"problems,":[75],"respectively.":[76],"Unlike":[77],"networks,":[80],"penalty":[82],"parameters,":[83],"problem,":[90],"guaranteed":[95],"converge":[97],"globally":[98],"exact":[101],"optimal":[102],"solution":[103],"without":[104],"any":[105],"additional":[106],"condition.":[107],"Compared":[108],"conventional":[110],"numerical":[111],"algorithms,":[112],"has":[116],"low":[118],"computational":[119],"complexity":[120],"can":[122,139],"deal":[123],"problem":[128],"degeneracy.":[130],"Several":[131],"applied":[132],"examples":[133],"show":[134],"that":[135],"obtain":[140],"more":[141],"accurate":[142],"estimates":[143],"than":[144],"several":[145],"algorithms.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2016-06-24T00:00:00"}