{"id":"https://openalex.org/W1992228381","doi":"https://doi.org/10.1117/12.131447","title":"New variants of the POCS method using affine subspaces of finite codimension with applications to irregular sampling","display_name":"New variants of the POCS method using affine subspaces of finite codimension with applications to irregular sampling","publication_year":1992,"publication_date":"1992-11-01","ids":{"openalex":"https://openalex.org/W1992228381","doi":"https://doi.org/10.1117/12.131447","mag":"1992228381"},"language":"en","primary_location":{"id":"doi:10.1117/12.131447","doi":"https://doi.org/10.1117/12.131447","is_oa":false,"landing_page_url":"https://doi.org/10.1117/12.131447","pdf_url":null,"source":{"id":"https://openalex.org/S183492911","display_name":"Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE","issn_l":"0277-786X","issn":["0277-786X","1996-756X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1"],"host_organization":"https://openalex.org/P4310315543","host_organization_name":"SPIE","host_organization_lineage":["https://openalex.org/P4310315543"],"host_organization_lineage_names":["SPIE"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SPIE Proceedings","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","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/A5016044961","display_name":"Hans Georg Feichtinger","orcid":"https://orcid.org/0000-0002-9927-0742","observed_orcids":["https://orcid.org/0000-0002-9927-0742"]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hans G. Feichtinger","raw_affiliation_strings":["Univ. Wien (Austria)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Wien (Austria)","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088825713","display_name":"Christian Cenker","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"C. Cenker","raw_affiliation_strings":["Univ. Wien (Austria)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Wien (Austria)","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022230972","display_name":"Monika Mayer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"M. Mayer","raw_affiliation_strings":["Univ. Wien (Austria)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Wien (Austria)","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007204077","display_name":"H. Steier","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"H. Steier","raw_affiliation_strings":["Univ. Wien (Austria)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Wien (Austria)","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080565728","display_name":"Thomas Strohmer","orcid":"https://orcid.org/0000-0003-2029-3317","observed_orcids":["https://orcid.org/0000-0003-2029-3317"]},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Thomas Strohmer","raw_affiliation_strings":["Univ. Wien (Austria)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Wien (Austria)","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":0.8084,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.64032258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"1818","issue":null,"first_page":"299","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.48510000109672546,"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":0.48510000109672546,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.3767000138759613,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.12039999663829803,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/projection-onto-convex-sets","display_name":"projection onto convex sets","score":0.9559999704360962},{"id":"https://openalex.org/keywords/non-uniform-sampling","display_name":"non-uniform sampling","score":0.8560000061988831},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"iterative reconstruction","score":0.47699999809265137},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.7289999723434448},{"id":"https://openalex.org/keywords/2d-image-reconstruction","display_name":"2D image reconstruction","score":0.6570000052452087}],"concepts":[{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.7367510795593262},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6774362921714783},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6605385541915894},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.64332515001297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6264797449111938},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6163313984870911},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5392042994499207},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5119653940200806},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41463935375213623},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.41284337639808655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34741514921188354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33555281162261963},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2951390743255615},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17098098993301392},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14897087216377258},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.138413667678833},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1190544068813324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1095353364944458},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1117/12.131447","doi":"https://doi.org/10.1117/12.131447","is_oa":false,"landing_page_url":"https://doi.org/10.1117/12.131447","pdf_url":null,"source":{"id":"https://openalex.org/S183492911","display_name":"Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE","issn_l":"0277-786X","issn":["0277-786X","1996-756X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1"],"host_organization":"https://openalex.org/P4310315543","host_organization_name":"SPIE","host_organization_lineage":["https://openalex.org/P4310315543"],"host_organization_lineage_names":["SPIE"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SPIE Proceedings","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322325","display_name":"Oesterreichische Nationalbank","ror":"https://ror.org/00nkcmy90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1625216228","https://openalex.org/W2040855018","https://openalex.org/W2051933044","https://openalex.org/W2137849144","https://openalex.org/W2143441774"],"related_works":["https://openalex.org/W4311408240","https://openalex.org/W3134400463","https://openalex.org/W2058574978","https://openalex.org/W2534945047","https://openalex.org/W194320125","https://openalex.org/W2542301877","https://openalex.org/W2076455116","https://openalex.org/W2747626117","https://openalex.org/W7097268996","https://openalex.org/W2185199774"],"abstract_inverted_index":{"The":[0],"POCS-method":[1,26],"(projection":[2],"onto":[3,43],"convex":[4],"subsets)":[5],"has":[6],"been":[7],"proposed":[8],"as":[9],"an":[10],"efficient":[11,94],"way":[12],"of":[13,38,41,65,90,96,110,114,127,131],"recovering":[14],"a":[15,33,39,111],"band-limited":[16],"signal":[17],"from":[18],"irregular":[19],"sampling":[20,30,53,66,115,132],"values.":[21],"However,":[22],"both":[23],"the":[24,47,56,63,88,97,122],"ordinary":[25],"(which":[27,50],"uses":[28,51],"one":[29,79],"point":[31],"at":[32,55,117],"given":[34],"time,":[35],"i.e.":[36],"consists":[37],"succession":[40],"projections":[42],"affine":[44],"hyperplanes)":[45],"and":[46],"one-step":[48],"method":[49,99],"all":[52],"values":[54],"same":[57],"time)":[58],"become":[59],"extremely":[60],"slow":[61],"if":[62],"number":[64,113],"points":[67,116,133],"gets":[68],"large.":[69],"Already":[70],"for":[71,161],"midsize":[72],"2D-problems":[73],"(e.g.":[74],"128":[75,77],"X":[76],"images)":[78],"may":[80],"easy":[81],"run":[82],"into":[83],"memory":[84],"problems.":[85],"Based":[86],"on":[87,121,158],"theory":[89],"pseudo-inverse":[91],"matrices":[92],"new":[93],"variants":[95],"POCS-":[98],"(so":[100],"to":[101,152],"say":[102],"intermediate":[103],"versions)":[104],"are":[105],"described,":[106],"which":[107],"make":[108],"use":[109],"finite":[112],"each":[118],"step.":[119],"Depending":[120],"computational":[123],"environment":[124],"appropriate":[125],"strategies":[126],"designing":[128],"those":[129],"families":[130,136,142,147],"(either":[134],"many":[135,144],"with":[137,143],"few":[138,141],"points,":[139,145],"or":[140,148],"overlapping":[146],"disjoint":[149],"ones...)":[150],"have":[151],"be":[153],"found.":[154],"We":[155],"also":[156],"report":[157],"numerical":[159],"results":[160],"these":[162],"algorithms.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}