{"id":"https://openalex.org/W2169006540","doi":"https://doi.org/10.1109/tnn.2009.2025500","title":"Complex-Valued Multistate Associative Memory With Nonlinear Multilevel Functions for Gray-Level Image Reconstruction","display_name":"Complex-Valued Multistate Associative Memory With Nonlinear Multilevel Functions for Gray-Level Image Reconstruction","publication_year":2009,"publication_date":"2009-07-30","ids":{"openalex":"https://openalex.org/W2169006540","doi":"https://doi.org/10.1109/tnn.2009.2025500","mag":"2169006540","pmid":"https://pubmed.ncbi.nlm.nih.gov/19643705"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2009.2025500","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2009.2025500","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","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/A5025420478","display_name":"Gouhei Tanaka","orcid":"https://orcid.org/0000-0002-6223-4406"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"G. Tanaka","raw_affiliation_strings":["Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan. gouhei@sat.t.u-tokyo.ac.jp","Institute of Industrial Science, University of Tokyo, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan. gouhei@sat.t.u-tokyo.ac.jp","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"Institute of Industrial Science, University of Tokyo, Tokyo, Japan","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038078845","display_name":"Kazuyuki Aihara","orcid":"https://orcid.org/0000-0002-4602-9816"},"institutions":[{"id":"https://openalex.org/I4210086780","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19","country_code":"JP","type":"government","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210086780"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"K. Aihara","raw_affiliation_strings":["ERATO Aihara Complexity Modelling Project, Japan Science and Technology Agency, Tokyo, Japan","Institute of Industrial Science, University of Tokyo, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ERATO Aihara Complexity Modelling Project, Japan Science and Technology Agency, Tokyo, Japan","institution_ids":["https://openalex.org/I4210086780"]},{"raw_affiliation_string":"Institute of Industrial Science, University of Tokyo, Tokyo, Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.374,"has_fulltext":false,"cited_by_count":183,"citation_normalized_percentile":{"value":0.97439378,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"20","issue":"9","first_page":"1463","last_page":"1473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9997000098228455,"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/T10320","display_name":"Neural Networks and Applications","score":0.9997000098228455,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9932000041007996,"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"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/sigmoid-function","display_name":"Sigmoid function","score":0.8434178829193115},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.8166306614875793},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"Content-addressable memory","score":0.7277693748474121},{"id":"https://openalex.org/keywords/hopfield-network","display_name":"Hopfield network","score":0.7196947932243347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6692278385162354},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.6335530281066895},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5681132674217224},{"id":"https://openalex.org/keywords/bidirectional-associative-memory","display_name":"Bidirectional associative memory","score":0.5374574661254883},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4861873984336853},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4825962781906128},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43966323137283325},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3778464198112488},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3696352243423462},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29603222012519836},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08112061023712158}],"concepts":[{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.8434178829193115},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.8166306614875793},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.7277693748474121},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.7196947932243347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6692278385162354},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6335530281066895},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5681132674217224},{"id":"https://openalex.org/C120620853","wikidata":"https://www.wikidata.org/wiki/Q506355","display_name":"Bidirectional associative memory","level":4,"score":0.5374574661254883},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4861873984336853},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4825962781906128},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43966323137283325},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3778464198112488},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3696352243423462},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29603222012519836},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08112061023712158},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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":"D001245","descriptor_name":"Association Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":true},{"descriptor_ui":"D001245","descriptor_name":"Association Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":true},{"descriptor_ui":"D001245","descriptor_name":"Association Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":true},{"descriptor_ui":"D003116","descriptor_name":"Color","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003116","descriptor_name":"Color","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003116","descriptor_name":"Color","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007091","descriptor_name":"Image Processing, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":true},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":true},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":true},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D010507","descriptor_name":"Periodicity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D010507","descriptor_name":"Periodicity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D010507","descriptor_name":"Periodicity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011939","descriptor_name":"Mental Recall","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D011939","descriptor_name":"Mental Recall","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D011939","descriptor_name":"Mental Recall","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","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},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnn.2009.2025500","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2009.2025500","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},{"id":"pmid:19643705","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19643705","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":"IEEE transactions on neural networks","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":27,"referenced_works":["https://openalex.org/W93167102","https://openalex.org/W639538290","https://openalex.org/W1481099253","https://openalex.org/W1970290902","https://openalex.org/W1971124072","https://openalex.org/W2010807387","https://openalex.org/W2047515252","https://openalex.org/W2068412593","https://openalex.org/W2079903808","https://openalex.org/W2085536277","https://openalex.org/W2096862483","https://openalex.org/W2106501603","https://openalex.org/W2107697999","https://openalex.org/W2107721470","https://openalex.org/W2123113196","https://openalex.org/W2126944419","https://openalex.org/W2128084896","https://openalex.org/W2132672282","https://openalex.org/W2136892987","https://openalex.org/W2146175204","https://openalex.org/W2153342234","https://openalex.org/W2161193272","https://openalex.org/W2161780063","https://openalex.org/W2164737680","https://openalex.org/W2487295360","https://openalex.org/W2541538937","https://openalex.org/W4214585779"],"related_works":["https://openalex.org/W4321273133","https://openalex.org/W1536116856","https://openalex.org/W2109892802","https://openalex.org/W2769111744","https://openalex.org/W2390617758","https://openalex.org/W2144581752","https://openalex.org/W2147932521","https://openalex.org/W2050720944","https://openalex.org/W2260028708","https://openalex.org/W1560986979"],"abstract_inverted_index":{"A":[0],"widely":[1],"used":[2],"complex-valued":[3,7,36,66,88,101],"activation":[4,37,67],"function":[5,27,68,95],"for":[6,75],"multistate":[8,55,77],"Hopfield":[9,89],"networks":[10,85,90,116],"is":[11,40,96,123],"revealed":[12],"to":[13,64,132],"be":[14],"essentially":[15],"based":[16,41],"on":[17,42,50],"a":[18,43,51,54,76,100,104],"multilevel":[19,25,30,44,93],"step":[20,26,94],"function.":[21],"By":[22],"replacing":[23],"the":[24,48,65,83,87,92,111,114],"with":[28,91,127],"other":[29,49,128],"characteristics,":[31],"we":[32],"present":[33],"two":[34],"alternative":[35],"functions.":[38],"One":[39],"sigmoid":[45],"function,":[46],"while":[47],"characteristic":[52],"of":[53,82,107,113],"bifurcating":[56],"neuron.":[57],"Numerical":[58],"experiments":[59],"show":[60],"that":[61],"both":[62],"modifications":[63],"bring":[69],"about":[70],"improvements":[71],"in":[72,117,125],"network":[73],"performance":[74,112],"associative":[78,130],"memory.":[79],"The":[80],"advantage":[81],"proposed":[84,115],"over":[86],"more":[97],"outstanding":[98],"when":[99],"neuron":[102],"represents":[103],"larger":[105],"number":[106],"multivalued":[108],"states.":[109],"Further,":[110],"reconstructing":[118],"noisy":[119],"256":[120],"gray-level":[121],"images":[122],"demonstrated":[124],"comparison":[126],"recent":[129],"memories":[131],"clarify":[133],"their":[134],"advantages":[135],"and":[136],"disadvantages.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":22},{"year":2020,"cited_by_count":22},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}