{"id":"https://openalex.org/W1970268217","doi":"https://doi.org/10.1109/tassp.1987.1165076","title":"Low rank detectors for Gaussian random vectors","display_name":"Low rank detectors for Gaussian random vectors","publication_year":1987,"publication_date":"1987-11-01","ids":{"openalex":"https://openalex.org/W1970268217","doi":"https://doi.org/10.1109/tassp.1987.1165076","mag":"1970268217"},"language":"en","primary_location":{"id":"doi:10.1109/tassp.1987.1165076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1987.1165076","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and 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/A5080469112","display_name":"Louis L. Scharf","orcid":"https://orcid.org/0000-0003-1764-9335"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Scharf","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112947264","display_name":"Barry Van Veen","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Van Veen","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":0.4946,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.58357014,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"35","issue":"11","first_page":"1579","last_page":"1582"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9745000004768372,"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/rank","display_name":"Rank (graph theory)","score":0.7873168587684631},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7833409309387207},{"id":"https://openalex.org/keywords/detector","display_name":"Detector","score":0.7210909724235535},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6339868903160095},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5802208185195923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5758102536201477},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5377213358879089},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5070528984069824},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5056953430175781},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.4967251420021057},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4749322533607483},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.47445735335350037},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46156659722328186},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4072537422180176},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3848085105419159},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2804735600948334},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24666571617126465},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24530619382858276},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20431742072105408},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16619661450386047},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06431940197944641},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05649992823600769}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7873168587684631},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7833409309387207},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.7210909724235535},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6339868903160095},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5802208185195923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5758102536201477},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5377213358879089},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5070528984069824},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5056953430175781},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4967251420021057},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4749322533607483},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.47445735335350037},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46156659722328186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4072537422180176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3848085105419159},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2804735600948334},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24666571617126465},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24530619382858276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20431742072105408},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16619661450386047},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06431940197944641},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05649992823600769},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tassp.1987.1165076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1987.1165076","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"},{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W218580582","https://openalex.org/W1536252645","https://openalex.org/W2118476648","https://openalex.org/W2123838014"],"related_works":["https://openalex.org/W94411513","https://openalex.org/W2377770720","https://openalex.org/W2113626999","https://openalex.org/W4311883357","https://openalex.org/W1990207062","https://openalex.org/W2886934452","https://openalex.org/W1489099099","https://openalex.org/W2024369332","https://openalex.org/W1974955043","https://openalex.org/W2160299300"],"abstract_inverted_index":{"A":[0],"constructive":[1],"procedure":[2,88],"is":[3],"presented":[4],"for":[5,78,89],"designing":[6],"low":[7],"rank":[8,53,92],"detectors":[9,24],"which":[10],"maximize":[11],"the":[12,17,28,38,48,52,55,91],"divergence":[13],"between":[14],"hypotheses":[15],"about":[16,47],"covariance":[18,49],"structure":[19,50],"of":[20,30,41,54,93],"Gaussian":[21],"signals.":[22],"The":[23],"are":[25,99],"constructed":[26],"from":[27],"eigenstructure":[29],"a":[31,86,94],"\"signal-to-noise":[32],"ratio\"":[33],"matrix.":[34],"We":[35],"show":[36,67],"that":[37,68],"unity":[39],"eigenvalues":[40,73],"this":[42],"matrix":[43],"provide":[44,75],"no":[45,61],"information":[46,77],"and":[51],"detector":[56],"may":[57,74],"be":[58],"reduced":[59],"with":[60],"performance":[62],"penalty.":[63],"More":[64],"generally,":[65],"we":[66],"in":[69],"certain":[70],"situations,":[71],"small":[72],"more":[76],"discrimination":[79],"than":[80],"large":[81],"eigenvalues.":[82],"This":[83],"leads":[84],"to":[85],"systematic":[87],"reducing":[90],"quadratic":[95],"detector.":[96],"Several":[97],"examples":[98],"discussed.":[100]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
