{"id":"https://openalex.org/W2949437887","doi":"https://doi.org/10.1109/tsp.2019.2922151","title":"Hypercomplex Widely Linear Estimation Through the Lens of Underpinning Geometry","display_name":"Hypercomplex Widely Linear Estimation Through the Lens of Underpinning Geometry","publication_year":2019,"publication_date":"2019-06-11","ids":{"openalex":"https://openalex.org/W2949437887","doi":"https://doi.org/10.1109/tsp.2019.2922151","mag":"2949437887"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2019.2922151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2922151","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-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/A5008618142","display_name":"Tohru Nitta","orcid":"https://orcid.org/0000-0001-9628-7920"},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Tohru Nitta","raw_affiliation_strings":["Human Informatics Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"Human Informatics Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Ibaraki, Japan","institution_ids":["https://openalex.org/I73613424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025747344","display_name":"Masaki Kobayashi","orcid":"https://orcid.org/0000-0002-4453-0615"},"institutions":[{"id":"https://openalex.org/I66906201","display_name":"University of Yamanashi","ror":"https://ror.org/059x21724","country_code":"JP","type":"education","lineage":["https://openalex.org/I66906201"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masaki Kobayashi","raw_affiliation_strings":["Mathematical Science Center, Yamanashi University, Yamanashi, Japan"],"affiliations":[{"raw_affiliation_string":"Mathematical Science Center, Yamanashi University, Yamanashi, Japan","institution_ids":["https://openalex.org/I66906201"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103001848","display_name":"Danilo P. Mandic","orcid":"https://orcid.org/0000-0001-8432-3963"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Danilo P. Mandic","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008618142"],"corresponding_institution_ids":["https://openalex.org/I73613424"],"apc_list":null,"apc_paid":null,"fwci":4.6534,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.95547917,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"67","issue":"15","first_page":"3985","last_page":"3994"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9979000091552734,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/quaternion","display_name":"Quaternion","score":0.8700801730155945},{"id":"https://openalex.org/keywords/hypercomplex-number","display_name":"Hypercomplex number","score":0.6955894827842712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6559963226318359},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5524470210075378},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5084125399589539},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.4595886468887329},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43859145045280457},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3987073004245758},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1438797116279602},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11731743812561035},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11394369602203369}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8700801730155945},{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.6955894827842712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6559963226318359},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5524470210075378},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5084125399589539},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.4595886468887329},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43859145045280457},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3987073004245758},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1438797116279602},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11731743812561035},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11394369602203369}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2019.2922151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2922151","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W579061","https://openalex.org/W565274834","https://openalex.org/W592889898","https://openalex.org/W595093130","https://openalex.org/W639989723","https://openalex.org/W776779855","https://openalex.org/W1897251165","https://openalex.org/W1965914766","https://openalex.org/W1968629980","https://openalex.org/W1987730473","https://openalex.org/W2067489830","https://openalex.org/W2069222481","https://openalex.org/W2081141244","https://openalex.org/W2095954570","https://openalex.org/W2098918476","https://openalex.org/W2099057098","https://openalex.org/W2108704185","https://openalex.org/W2114765937","https://openalex.org/W2128552251","https://openalex.org/W2128771710","https://openalex.org/W2134563598","https://openalex.org/W2136580750","https://openalex.org/W2157910179","https://openalex.org/W2161397505","https://openalex.org/W2476841360","https://openalex.org/W2497204217","https://openalex.org/W2536893788","https://openalex.org/W2587219380","https://openalex.org/W2599542682","https://openalex.org/W2780313524","https://openalex.org/W2900590900","https://openalex.org/W4211251910","https://openalex.org/W4235693166","https://openalex.org/W4301374466","https://openalex.org/W6615947857"],"related_works":["https://openalex.org/W2916518000","https://openalex.org/W2916498667","https://openalex.org/W2917906954","https://openalex.org/W2572893131","https://openalex.org/W2917330019","https://openalex.org/W2917006597","https://openalex.org/W2916884673","https://openalex.org/W1897251165","https://openalex.org/W2423267406","https://openalex.org/W2020324309"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2,46,56,60],"rigorous":[3],"account":[4,35],"of":[5,36,38,135,155,158],"the":[6,9,16,68,71,76,82,87,94,113,133,152,156,159],"equivalence":[7],"between":[8,45],"complex-valued":[10,72,77],"widely":[11,19,78,97,161],"linear":[12,20,27,73,79,84,90,98,115,162],"estimation":[13,21,28,74,80,85,91,99,116,136,163],"method":[14,22,100],"and":[15,40,49,55,93,109,130],"quaternion":[17,57,83,88,95],"involution":[18,96],"with":[23],"their":[24,143],"vector-valued":[25],"real":[26,53,62,145],"counterparts.":[29,147],"This":[30,123],"is":[31],"achieved":[32],"by":[33,41],"an":[34,50],"degrees":[37],"freedom":[39],"providing":[42],"matrix":[43],"mappings":[44],"complex":[47,107],"variable":[48,58],"isomorphic":[51],"bivariate":[52],"vector,":[54],"versus":[59],"quadri-variate":[61],"vector.":[63],"Furthermore,":[64],"we":[65,150],"show":[66],"that":[67],"parameters":[69],"in":[70,128,137],"method,":[75,81,86,92],"semi-widely":[89],"include":[101],"distinct":[102],"geometric":[103],"structures":[104],"imposed":[105],"on":[106],"numbers":[108],"quaternions,":[110],"respectively,":[111],"whereas":[112],"real-valued":[114],"methods":[117],"do":[118],"not":[119],"exhibit":[120],"any":[121],"structure.":[122],"key":[124],"difference":[125],"explains,":[126],"both":[127],"theoretical":[129],"practical":[131],"terms,":[132],"advantage":[134],"division":[138],"algebras":[139],"(complex,":[140],"quaternion)":[141],"over":[142],"multivariate":[144],"vector":[146],"In":[148],"addition,":[149],"discuss":[151],"computational":[153],"complexities":[154],"estimators":[157],"hypercomplex":[160],"methods.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
