{"id":"https://openalex.org/W2170897209","doi":"https://doi.org/10.1109/tac.2011.2125050","title":"A Maximum Entropy Solution of the Covariance Extension Problem for Reciprocal Processes","display_name":"A Maximum Entropy Solution of the Covariance Extension Problem for Reciprocal Processes","publication_year":2011,"publication_date":"2011-03-15","ids":{"openalex":"https://openalex.org/W2170897209","doi":"https://doi.org/10.1109/tac.2011.2125050","mag":"2170897209"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2011.2125050","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2125050","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1101.4849","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Francesca P. Carli","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesca P. Carli","raw_affiliation_strings":["Department of Information Engineering (DEI), University of Padova, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Engineering (DEI), University of Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Augusto Ferrante","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Augusto Ferrante","raw_affiliation_strings":["Department of Information Engineering (DEI), University of Padova, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Engineering (DEI), University of Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Michele Pavon","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Michele Pavon","raw_affiliation_strings":["Department of Pure and Applied Mathematics, University of Padova, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Mathematics, University of Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":null,"display_name":"Giorgio Picci","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giorgio Picci","raw_affiliation_strings":["Department of Information Engineering (DEI), University of Padova, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Engineering (DEI), University of Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":null,"apc_paid":null,"fwci":3.2987,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.9266814,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"9","first_page":"1999","last_page":"2012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.20149999856948853,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.20149999856948853,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.07880000025033951,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.07270000129938126,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.7936000227928162},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.7522000074386597},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.5439000129699707},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5242000222206116},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.5012000203132629},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.42899999022483826},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.42149999737739563},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.40470001101493835},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.3944000005722046}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.7936000227928162},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.7522000074386597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6531999707221985},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.5439000129699707},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5242000222206116},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.5012000203132629},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4465999901294708},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.42899999022483826},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.40470001101493835},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C110405555","wikidata":"https://www.wikidata.org/wiki/Q1192209","display_name":"Stationary process","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.3449000120162964},{"id":"https://openalex.org/C98735484","wikidata":"https://www.wikidata.org/wiki/Q186971","display_name":"Time reversibility","level":5,"score":0.33880001306533813},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33340001106262207},{"id":"https://openalex.org/C79610928","wikidata":"https://www.wikidata.org/wiki/Q1656743","display_name":"Parameter identification problem","level":3,"score":0.32100000977516174},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.310699999332428},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.3075999915599823},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C18436578","wikidata":"https://www.wikidata.org/wiki/Q7604346","display_name":"Stationary sequence","level":3,"score":0.2784000039100647},{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.2648000121116638},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.26330000162124634}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2011.2125050","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2125050","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1101.4849","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1101.4849","pdf_url":"https://arxiv.org/pdf/1101.4849","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:www.research.unipd.it:11577/119106","is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5727914","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1101.4849","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1101.4849","pdf_url":"https://arxiv.org/pdf/1101.4849","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2170897209.pdf","grobid_xml":"https://content.openalex.org/works/W2170897209.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W173134094","https://openalex.org/W1965077150","https://openalex.org/W1995875735","https://openalex.org/W2012507373","https://openalex.org/W2016794928","https://openalex.org/W2057034079","https://openalex.org/W2063084473","https://openalex.org/W2064547027","https://openalex.org/W2073708660","https://openalex.org/W2089598668","https://openalex.org/W2107453951","https://openalex.org/W2115125420","https://openalex.org/W2116499526","https://openalex.org/W2131876911","https://openalex.org/W2140505091","https://openalex.org/W2141419326","https://openalex.org/W2141844446","https://openalex.org/W2157273492","https://openalex.org/W2160664904","https://openalex.org/W2165177477","https://openalex.org/W2299620045","https://openalex.org/W2326591006","https://openalex.org/W3000400773","https://openalex.org/W4236270661","https://openalex.org/W4238253035","https://openalex.org/W4241513305","https://openalex.org/W4388396077","https://openalex.org/W6679489882","https://openalex.org/W6699466363"],"related_works":[],"abstract_inverted_index":{"Stationary":[0,66],"reciprocal":[1,28,67,70,129],"processes":[2,29,68,130,154,175],"defined":[3],"on":[4,176,186],"a":[5,16,83,126,157,198,218],"finite":[6,84],"interval":[7],"of":[8,19,44,86,95,128,136,152,221],"the":[9,35,45,49,64,87,133,167,177,182,187,190,206,212,222],"integer":[10,178,188],"line":[11],"can":[12,110],"be":[13,105,197],"seen":[14],"as":[15],"special":[17],"class":[18,127],"Markov":[20],"random":[21],"fields":[22],"restricted":[23],"to":[24,48,56,104,112,156,196,217],"one":[25],"dimension.":[26],"Nonstationary":[27],"have":[30,57],"been":[31,58],"extensively":[32],"studied":[33],"in":[34,60,63,82,116,141,181,204],"past":[36],"especially":[37],"by":[38],"Jamison":[39],"et":[40],"al.":[41],"The":[42],"specialization":[43],"nonstationary":[46],"theory":[47],"stationary":[50,174,184],"case,":[51],"however,":[52],"does":[53],"not":[54],"seem":[55],"pursued":[59],"sufficient":[61],"depth":[62],"literature.":[65],"(and":[69],"stochastic":[71],"models)":[72],"are":[73],"potentially":[74],"useful":[75],"for":[76,161,173],"describing":[77],"signals":[78],"which":[79,109,131],"naturally":[80],"live":[81],"region":[85],"time":[88],"(or":[89],"space)":[90],"line.":[91,179],"Estimation":[92],"or":[93],"identification":[94,151,207],"these":[96,153],"models":[97],"starting":[98],"from":[99],"observed":[100],"data":[101],"seems":[102],"still":[103],"an":[106],"open":[107],"problem":[108,160,172,193],"lead":[111],"many":[113],"interesting":[114],"applications":[115],"signal":[117,144],"and":[118,143,201],"image":[119],"processing.":[120,145],"In":[121],"this":[122],"paper,":[123],"we":[124],"discuss":[125],"is":[132],"acausal":[134],"analog":[135],"auto-regressive":[137],"(AR)":[138],"processes,":[139],"familiar":[140],"control":[142],"We":[146,209],"show":[147,210],"that":[148,211],"maximum":[149,213],"likelihood":[150],"leads":[155,216],"covariance":[158,163,169,191],"extension":[159,171,192],"block-circulant":[162],"matrices.":[164],"This":[165],"generalizes":[166],"famous":[168],"band":[170],"As":[180],"usual":[183],"setting":[185],"line,":[189],"turns":[194],"out":[195],"basic":[199],"conceptual":[200],"practical":[202],"step":[203],"solving":[205],"problem.":[208,223],"entropy":[214],"principle":[215],"complete":[219],"solution":[220]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
