{"id":"https://openalex.org/W2765328919","doi":"https://doi.org/10.23919/eusipco.2017.8081398","title":"Constrained subspace estimation via convex optimization","display_name":"Constrained subspace estimation via convex optimization","publication_year":2017,"publication_date":"2017-08-01","ids":{"openalex":"https://openalex.org/W2765328919","doi":"https://doi.org/10.23919/eusipco.2017.8081398","mag":"2765328919"},"language":"en","primary_location":{"id":"doi:10.23919/eusipco.2017.8081398","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2017.8081398","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 25th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10902/13017","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059078809","display_name":"Ignacio Santamar\u0131\u0301a","orcid":"https://orcid.org/0000-0003-0040-7436"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"I. Santamaria","raw_affiliation_strings":["Dept. Ingenieria de Comunicaciones, Universidad de Cantabria Plaza de la Ciencia, Santander, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. Ingenieria de Comunicaciones, Universidad de Cantabria Plaza de la Ciencia, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071269640","display_name":"Javier V\u00eda","orcid":"https://orcid.org/0000-0001-7853-0069"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. Via","raw_affiliation_strings":["Dept. Ingenieria de Comunicaciones, Universidad de Cantabria Plaza de la Ciencia, Santander, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. Ingenieria de Comunicaciones, Universidad de Cantabria Plaza de la Ciencia, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061567476","display_name":"Michael Kirby","orcid":"https://orcid.org/0000-0001-9802-9263"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Kirby","raw_affiliation_strings":["Department of Mathematics, Colorado State University, Fort Collins, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024418285","display_name":"Tim Marrinan","orcid":"https://orcid.org/0000-0001-5240-3053"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Marrinan","raw_affiliation_strings":["Colorado State University, Fort Collins, CO, US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Colorado State University, Fort Collins, CO, US","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078621088","display_name":"Chris Peterson","orcid":"https://orcid.org/0000-0002-3982-6876"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Peterson","raw_affiliation_strings":["Department of Mathematics, Colorado State University, Fort Collins, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080469112","display_name":"Louis L. Scharf","orcid":"https://orcid.org/0000-0003-1764-9335"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Scharf","raw_affiliation_strings":["Department of Mathematics, Colorado State University, Fort Collins, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1200","last_page":"1204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9998000264167786,"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/T10860","display_name":"Speech and Audio Processing","score":0.9965999722480774,"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/T11946","display_name":"Antenna Design and Optimization","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/subspace-topology","display_name":"Subspace topology","score":0.894059419631958},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7421960234642029},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6547860503196716},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6007369756698608},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.5205234289169312},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5185247659683228},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4938298165798187},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4891689121723175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4523641765117645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42629989981651306},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4261499345302582},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41995179653167725},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15710589289665222},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06392508745193481}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.894059419631958},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7421960234642029},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6547860503196716},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6007369756698608},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.5205234289169312},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5185247659683228},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4938298165798187},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4891689121723175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4523641765117645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42629989981651306},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4261499345302582},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41995179653167725},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15710589289665222},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06392508745193481},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.23919/eusipco.2017.8081398","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2017.8081398","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 25th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},{"id":"pmh:oai:repositorio.unican.es:10902/13017","is_oa":true,"landing_page_url":"http://hdl.handle.net/10902/13017","pdf_url":null,"source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th European Signal Processing Conference (EUSIPCO), Kos island, Greece, 2017, 1200-1204","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:repositorio.unican.es:10902/13017","is_oa":true,"landing_page_url":"http://hdl.handle.net/10902/13017","pdf_url":null,"source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th European Signal Processing Conference (EUSIPCO), Kos island, Greece, 2017, 1200-1204","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1217030947","display_name":"BIGDATA: F: Data Driven Optimization on Flag Manifolds with Geometric Constraints","funder_award_id":"1633830","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2203312256","display_name":null,"funder_award_id":"TEC2016-81900","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"},{"id":"https://openalex.org/G8874561142","display_name":null,"funder_award_id":"TEC2016-81900-REDT","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320326262","display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a","ror":"https://ror.org/03sv46s19"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1996215314","https://openalex.org/W2036161092","https://openalex.org/W2045512849","https://openalex.org/W2069175399","https://openalex.org/W2093229781","https://openalex.org/W2117920736","https://openalex.org/W2121847472","https://openalex.org/W2149338181","https://openalex.org/W2156529323","https://openalex.org/W2162654459","https://openalex.org/W2165207694","https://openalex.org/W2166167085","https://openalex.org/W2167208435","https://openalex.org/W2171656554","https://openalex.org/W2336767348","https://openalex.org/W2501240968","https://openalex.org/W2509499822"],"related_works":["https://openalex.org/W3100286349","https://openalex.org/W2896134808","https://openalex.org/W4289378085","https://openalex.org/W4294291164","https://openalex.org/W3172436493","https://openalex.org/W1887135636","https://openalex.org/W4287164812","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W3213150849"],"abstract_inverted_index":{"Given":[0],"a":[1,9,19,35,86],"collection":[2],"of":[3,17,38,62,90,96],"M":[4],"experimentally":[5],"measured":[6],"subspaces,":[7],"and":[8,80,106],"model-based":[10,32,54],"subspace,":[11],"this":[12,70,91],"paper":[13],"addresses":[14],"the":[15,23,26,31,53,60,67,74,97],"problem":[16,45],"finding":[18],"subspace":[20,33,42,55,76],"that":[21,28],"approximates":[22],"collection,":[24],"under":[25],"constraint":[27],"it":[29],"intersects":[30],"in":[34,47],"predetermined":[36],"number":[37],"dimensions.":[39],"This":[40],"constrained":[41,75],"estimation":[43,77],"(CSE)":[44,78],"arises":[46],"applications":[48],"such":[49],"as":[50],"beamforming,":[51],"where":[52],"encodes":[56],"prior":[57],"information":[58],"about":[59],"direction-of-arrival":[61],"some":[63],"sources":[64],"impinging":[65],"on":[66,85],"array.":[68],"In":[69],"paper,":[71],"we":[72],"formulate":[73],"problem,":[79],"present":[81],"an":[82],"approximation":[83],"based":[84],"semidefinite":[87],"relaxation":[88],"(SDR)":[89],"non-convex":[92],"problem.":[93],"The":[94],"performance":[95],"proposed":[98],"CSE":[99],"algorithm":[100],"is":[101,111],"demonstrated":[102],"via":[103],"numerical":[104],"simulation,":[105],"its":[107],"application":[108],"to":[109],"beamforming":[110],"also":[112],"discussed.":[113]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2017-11-10T00:00:00"}
