{"id":"https://openalex.org/W1965457516","doi":"https://doi.org/10.1109/globalsip.2013.6736960","title":"Projections onto convex sets (POCS) based optimization by lifting","display_name":"Projections onto convex sets (POCS) based optimization by lifting","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W1965457516","doi":"https://doi.org/10.1109/globalsip.2013.6736960","mag":"1965457516"},"language":"en","primary_location":{"id":"doi:10.1109/globalsip.2013.6736960","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globalsip.2013.6736960","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Global Conference on Signal and Information Processing","raw_type":"proceedings-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/A5113644545","display_name":"A. Enis \u00c7etin","orcid":"https://orcid.org/0009-0009-7700-7124"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"A. Enis Cetin","raw_affiliation_strings":["Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]},{"raw_affiliation_string":"Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053808736","display_name":"Alican Bozkurt","orcid":"https://orcid.org/0000-0002-3796-7296"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"A. Bozkurt","raw_affiliation_strings":["Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]},{"raw_affiliation_string":"Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033894508","display_name":"Osman G\u00fcnay","orcid":"https://orcid.org/0000-0001-7131-2253"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"O. Gunay","raw_affiliation_strings":["Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]},{"raw_affiliation_string":"Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026726753","display_name":"Y. Hakan Habibo\u01e7lu","orcid":null},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Y. H. Habiboglu","raw_affiliation_strings":["Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]},{"raw_affiliation_string":"Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074048076","display_name":"K\u0131van\u00e7 K\u00f6se","orcid":"https://orcid.org/0000-0003-3185-2639"},"institutions":[{"id":"https://openalex.org/I1334819555","display_name":"Memorial Sloan Kettering Cancer Center","ror":"https://ror.org/02yrq0923","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1334819555"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. Kose","raw_affiliation_strings":["Dermatology Service, Memorial Sloan Kettering Cancer Center, New York","Dermatology Service, Memorial Sloan Kettering Cancer Center, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dermatology Service, Memorial Sloan Kettering Cancer Center, New York","institution_ids":["https://openalex.org/I1334819555"]},{"raw_affiliation_string":"Dermatology Service, Memorial Sloan Kettering Cancer Center, New York, NY, USA","institution_ids":["https://openalex.org/I1334819555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105231625","display_name":"\u0130brahim Onaran","orcid":"https://orcid.org/0000-0002-7769-4077"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"I. Onaran","raw_affiliation_strings":["Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]},{"raw_affiliation_string":"Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026535457","display_name":"Mohammad Tofighi","orcid":"https://orcid.org/0000-0002-3249-1399"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"M. Tofighi","raw_affiliation_strings":["Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]},{"raw_affiliation_string":"Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016291763","display_name":"R. Akin Sevimli","orcid":"https://orcid.org/0000-0002-3668-6943"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"R. A. Sevimli","raw_affiliation_strings":["Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department. of Electrical and Electronic Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]},{"raw_affiliation_string":"Dept. of Electr. & Electron Eng., Bilkent Univ., Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.6436,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.95973237,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"623","last_page":"623"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5900296568870544},{"id":"https://openalex.org/keywords/epigraph","display_name":"Epigraph","score":0.5592871904373169},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.5143474340438843},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5040101408958435},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.48955973982810974},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47599589824676514},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4759090542793274},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.47422313690185547},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4421064853668213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44185033440589905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4160696268081665},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4144400656223297},{"id":"https://openalex.org/keywords/ellipsoid-method","display_name":"Ellipsoid method","score":0.4116939902305603},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.41151729226112366},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4105333387851715},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40276026725769043},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37547117471694946},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.2278219759464264}],"concepts":[{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5900296568870544},{"id":"https://openalex.org/C17192189","wikidata":"https://www.wikidata.org/wiki/Q1347059","display_name":"Epigraph","level":2,"score":0.5592871904373169},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.5143474340438843},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5040101408958435},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.48955973982810974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47599589824676514},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4759090542793274},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.47422313690185547},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4421064853668213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44185033440589905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4160696268081665},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4144400656223297},{"id":"https://openalex.org/C205451395","wikidata":"https://www.wikidata.org/wiki/Q378574","display_name":"Ellipsoid method","level":5,"score":0.4116939902305603},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.41151729226112366},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4105333387851715},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40276026725769043},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37547117471694946},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2278219759464264},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/globalsip.2013.6736960","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globalsip.2013.6736960","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE Global Conference on Signal and Information Processing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.361.7407","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.7407","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://signal.ee.bilkent.edu.tr/Publications/pocs.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.765.5073","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.765.5073","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1306.2516.pdf","raw_type":"text"},{"id":"pmh:oai:repository.bilkent.edu.tr:11693/27908","is_oa":false,"landing_page_url":"http://hdl.handle.net/11693/27908","pdf_url":null,"source":{"id":"https://openalex.org/S4306400079","display_name":"Bilkent University Institutional Repository (Bilkent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I168864056","host_organization_name":"Bilkent University","host_organization_lineage":["https://openalex.org/I168864056"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2013 IEEE Global Conference on Signal and Information Processing","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1493250972","https://openalex.org/W1946620893","https://openalex.org/W1964365657","https://openalex.org/W1965341600","https://openalex.org/W1965457516","https://openalex.org/W1984958640","https://openalex.org/W1996287810","https://openalex.org/W2000748685","https://openalex.org/W2019794334","https://openalex.org/W2033468335","https://openalex.org/W2040319497","https://openalex.org/W2057176614","https://openalex.org/W2066333552","https://openalex.org/W2074872938","https://openalex.org/W2084263592","https://openalex.org/W2085440994","https://openalex.org/W2090991423","https://openalex.org/W2095962783","https://openalex.org/W2098514788","https://openalex.org/W2100108897","https://openalex.org/W2101447418","https://openalex.org/W2103559027","https://openalex.org/W2104266187","https://openalex.org/W2111395440","https://openalex.org/W2115908389","https://openalex.org/W2119667497","https://openalex.org/W2120985577","https://openalex.org/W2141937552","https://openalex.org/W2148894924","https://openalex.org/W2185916416","https://openalex.org/W2246091536","https://openalex.org/W2541970526","https://openalex.org/W2951185455"],"related_works":["https://openalex.org/W2340690432","https://openalex.org/W2439655505","https://openalex.org/W2985979428","https://openalex.org/W2510140549","https://openalex.org/W2187449906","https://openalex.org/W2962818859","https://openalex.org/W2319106417","https://openalex.org/W2569941367","https://openalex.org/W2089105401","https://openalex.org/W2154682027"],"abstract_inverted_index":{"Summary":[0],"form":[1],"only":[2],"given.":[3],"A":[4],"new":[5,165],"optimization":[6,23,83,116],"technique":[7],"based":[8,145,167],"on":[9,146],"the":[10,30,41,47,59,64,67,105,115,160],"projections":[11],"onto":[12,102],"convex":[13,19,52,73],"space":[14],"(POCS)":[15],"framework":[16],"for":[17],"solving":[18],"and":[20,37,96,133,176],"some":[21],"non-convex":[22],"problems":[24],"are":[25,44],"presented.":[26],"The":[27,81,118,164],"dimension":[28],"of":[29,66,104,114],"minimization":[31],"problem":[32],"is":[33,50,63,70,100,138],"lifted":[34],"by":[35,158],"one":[36,103],"sets":[38,106],"corresponding":[39,60],"to":[40],"cost":[42,48,68,135,143],"function":[43,49,53,69],"defined.":[45],"If":[46],"a":[51,72,108],"in":[54,75,91,107,124,172],"R":[55,76,92],"<sup":[56,77,93],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[57,78,94,130,149],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</sup>":[58],"set":[61,74],"which":[62],"epigraph":[65],"also":[71,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N+1</sup>":[79,95],".":[80],"iterative":[82],"approach":[84],"starts":[85],"with":[86],"an":[87,97],"arbitrary":[88],"initial":[89],"estimate":[90],"orthogonal":[98],"projection":[99],"performed":[101],"sequential":[109],"manner":[110],"at":[111],"each":[112],"step":[113],"problem.":[117],"method":[119,168],"provides":[120],"globally":[121],"optimal":[122],"solutions":[123],"total-variation,":[125],"filtered":[126],"variation,":[127],"l":[128,147],"<sub":[129,148],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[131],",":[132],"entropic":[134],"functions.":[136],"It":[137],"experimentally":[140],"observed":[141],"that":[142],"functions":[144],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[150],";":[151],"p":[152],"<;":[153],"1":[154],"may":[155],"be":[156,170],"handled":[157],"using":[159],"supporting":[161],"hyperplane":[162],"concept.":[163],"POCS":[166],"can":[169],"used":[171],"image":[173],"deblurring,":[174],"restoration":[175],"compressive":[177],"sensing":[178],"problems.":[179]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}