{"id":"https://openalex.org/W2101491646","doi":"https://doi.org/10.1109/tit.1967.1054035","title":"A projection method for signal detection in colored Gaussian noise","display_name":"A projection method for signal detection in colored Gaussian noise","publication_year":1967,"publication_date":"1967-07-01","ids":{"openalex":"https://openalex.org/W2101491646","doi":"https://doi.org/10.1109/tit.1967.1054035","mag":"2101491646"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1967.1054035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1967.1054035","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5014088470","display_name":"T. Kailath","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T. Kailath","raw_affiliation_strings":["Department of Electrical Engineering, University of Stanford, Stanford, CA, USA","Stanford University Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014088470"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":4.2774,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.93680615,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"3","first_page":"441","last_page":"447"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9986000061035156,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9958000183105469,"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":0.9926999807357788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.6693270206451416},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.66231369972229},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6022793054580688},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.569786012172699},{"id":"https://openalex.org/keywords/colors-of-noise","display_name":"Colors of noise","score":0.5559223890304565},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5505818724632263},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5460456013679504},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5451653599739075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5275663137435913},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5192963480949402},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5154710412025452},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5020127296447754},{"id":"https://openalex.org/keywords/orthographic-projection","display_name":"Orthographic projection","score":0.4885047674179077},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.45776158571243286},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4468972980976105},{"id":"https://openalex.org/keywords/series-expansion","display_name":"Series expansion","score":0.42791748046875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42003774642944336},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.41033026576042175},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3300168514251709},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.3261094093322754},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21488863229751587},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19682860374450684},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.10346445441246033},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07776176929473877}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.6693270206451416},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.66231369972229},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6022793054580688},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.569786012172699},{"id":"https://openalex.org/C114996537","wikidata":"https://www.wikidata.org/wiki/Q4854529","display_name":"Colors of noise","level":3,"score":0.5559223890304565},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5505818724632263},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5460456013679504},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5451653599739075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5275663137435913},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5192963480949402},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5154710412025452},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5020127296447754},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.4885047674179077},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.45776158571243286},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4468972980976105},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.42791748046875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42003774642944336},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.41033026576042175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3300168514251709},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.3261094093322754},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21488863229751587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19682860374450684},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.10346445441246033},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07776176929473877},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1967.1054035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1967.1054035","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1577906631","https://openalex.org/W1967894401","https://openalex.org/W1986280275","https://openalex.org/W1987916557","https://openalex.org/W1995382677","https://openalex.org/W2007641452","https://openalex.org/W2031782596","https://openalex.org/W2033584446","https://openalex.org/W2041029825","https://openalex.org/W2049917002","https://openalex.org/W2052398345","https://openalex.org/W2070579919","https://openalex.org/W2089438196","https://openalex.org/W2101988614","https://openalex.org/W2132959063","https://openalex.org/W4205447762","https://openalex.org/W4214907657"],"related_works":["https://openalex.org/W2018264451","https://openalex.org/W4212827636","https://openalex.org/W2384327295","https://openalex.org/W2591253179","https://openalex.org/W2101505280","https://openalex.org/W4287671600","https://openalex.org/W2141366819","https://openalex.org/W3004408979","https://openalex.org/W1968911901","https://openalex.org/W1700578922"],"abstract_inverted_index":{"The":[0,56,110,133],"problem":[1,92],"of":[2,5,48,51,53,58,75,88,99,117,141,148],"the":[3,19,25,67,73,90,100,103,139],"detection":[4,91],"known":[6],"signals":[7,20],"in":[8,144],"colored":[9],"Gaussian":[10],"noise":[11],"is":[12,29,61,70,81,135],"usually":[13],"studied":[14],"through":[15],"infinite-series":[16,36,104],"representations":[17],"for":[18,32],"and":[21,63,118],"noise.":[22],"In":[23],"particular,":[24],"Karhunen-Lo\u00e8ve":[26],"(K-L)":[27],"expansion":[28,69,106],"often":[30,40,82],"used":[31],"this":[33],"purpose.":[34],"Such":[35],"methods,":[37],"while":[38],"elegant,":[39],"introduce":[41],"mathematical":[42],"complications":[43],"because":[44],"they":[45],"raise":[46],"questions":[47],"convergence,":[49],"interchange":[50],"orders":[52],"integration,":[54],"etc.":[55],"resolution":[57],"these":[59],"problems":[60],"difficult":[62],"has":[64,127],"led,":[65],"when":[66],"K-L":[68,105],"used,":[71],"to":[72,93],"introduction":[74],"subsidiary":[76],"conditions":[77],"whose":[78],"physical":[79,120],"meaning":[80],"unclear.":[83],"We":[84],"present":[85],"a":[86,94,142,145,152],"method":[87,134],"reducing":[89],"finite-dimensional":[95],"form":[96],"where":[97],"many":[98],"difficulties":[101],"with":[102],"do":[107],"not":[108],"arise.":[109],"resulting":[111],"simplicity":[112],"provides":[113],"more":[114,119],"direct":[115],"derivations":[116],"insights":[121],"into":[122],"several":[123],"earlier":[124],"results.":[125,132],"It":[126],"also":[128],"suggested":[129],"some":[130],"new":[131],"essentially":[136],"based":[137],"on":[138],"use":[140],"projection":[143],"special":[146],"kind":[147],"Hilbert":[149,155],"space":[150],"called":[151],"reproducing":[153],"kernel":[154],"space.":[156]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}