{"id":"https://openalex.org/W2072951627","doi":"https://doi.org/10.1137/090767777","title":"Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming","display_name":"Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2072951627","doi":"https://doi.org/10.1137/090767777","mag":"2072951627","pmid":"https://pubmed.ncbi.nlm.nih.gov/22536457"},"language":"en","primary_location":{"id":"doi:10.1137/090767777","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090767777","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5062844820","display_name":"Amit Singer","orcid":"https://orcid.org/0000-0002-6975-7955"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Singer","raw_affiliation_strings":["Department of Mathematics and PACM, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000","amits@math.princeton.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and PACM, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"amits@math.princeton.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037804006","display_name":"Yoel Shkolnisky","orcid":"https://orcid.org/0000-0001-8784-3753"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Y. Shkolnisky","raw_affiliation_strings":["yoelsh@post.tau.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"yoelsh@post.tau.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062844820"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":14.1534,"has_fulltext":false,"cited_by_count":191,"citation_normalized_percentile":{"value":0.98669295,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"4","issue":"2","first_page":"543","last_page":"572"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10857","display_name":"Advanced Electron Microscopy Techniques and Applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1315","display_name":"Structural Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10857","display_name":"Advanced Electron Microscopy Techniques and Applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1315","display_name":"Structural Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12039","display_name":"Electron and X-Ray Spectroscopy Techniques","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9904999732971191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7645431160926819},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6952731609344482},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5759565234184265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5348604321479797},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5162979960441589},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4853304922580719},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.46370914578437805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34462523460388184},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.329551637172699}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7645431160926819},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6952731609344482},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5759565234184265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5348604321479797},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5162979960441589},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4853304922580719},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.46370914578437805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34462523460388184},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.329551637172699},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/090767777","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090767777","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmid:22536457","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22536457","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on imaging sciences","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.296.6815","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.6815","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.upenn.edu/~trietle/teaching/math584/reports/Singer_etal_cryo_em_2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.387.4018","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.387.4018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://web.math.princeton.edu/~amits/publications/common_lines.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.387.8393","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.387.8393","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://web.math.princeton.edu/~amits/publications/common_lines_revision2.pdf","raw_type":"text"},{"id":"pmh:oai:europepmc.org:2339197","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3334316","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W163597489","https://openalex.org/W636061944","https://openalex.org/W1967489089","https://openalex.org/W1983383403","https://openalex.org/W1983751391","https://openalex.org/W1985123706","https://openalex.org/W1987087256","https://openalex.org/W1988874269","https://openalex.org/W1993701054","https://openalex.org/W1999913571","https://openalex.org/W2000157792","https://openalex.org/W2020001524","https://openalex.org/W2024183250","https://openalex.org/W2032347855","https://openalex.org/W2043905980","https://openalex.org/W2048937426","https://openalex.org/W2049668823","https://openalex.org/W2058583833","https://openalex.org/W2059466049","https://openalex.org/W2061109699","https://openalex.org/W2066459185","https://openalex.org/W2078193953","https://openalex.org/W2085744431","https://openalex.org/W2088164510","https://openalex.org/W2090980101","https://openalex.org/W2097469960","https://openalex.org/W2099111195","https://openalex.org/W2100758571","https://openalex.org/W2105367101","https://openalex.org/W2112308043","https://openalex.org/W2116648916","https://openalex.org/W2116888204","https://openalex.org/W2124709258","https://openalex.org/W2142901448","https://openalex.org/W2143075842","https://openalex.org/W2143703915","https://openalex.org/W2147217411","https://openalex.org/W2149783883","https://openalex.org/W2150938882","https://openalex.org/W2155688047","https://openalex.org/W2157532189","https://openalex.org/W2328187444","https://openalex.org/W2499952289","https://openalex.org/W2912522929","https://openalex.org/W3007475603","https://openalex.org/W3103766153","https://openalex.org/W4243997607"],"related_works":["https://openalex.org/W1983756092","https://openalex.org/W2381295697","https://openalex.org/W2385886188","https://openalex.org/W579949368","https://openalex.org/W2092089517","https://openalex.org/W2378309693","https://openalex.org/W1788812054","https://openalex.org/W2288891047","https://openalex.org/W2934566931","https://openalex.org/W4288376261"],"abstract_inverted_index":{"The":[0],"cryo-electron":[1],"microscopy":[2],"reconstruction":[3],"problem":[4],"is":[5,48,64,79,117,140],"to":[6,61,82,207,237],"find":[7],"the":[8,39,54,57,70,83,88,99,112,115,121,133,137,150,178,195,221,226,231],"three-dimensional":[9],"(3D)":[10],"structure":[11,34],"of":[12,18,56,76,87,103,125,152,180],"a":[13,45,73,126,181,186,208,238],"macromolecule":[14],"given":[15],"noisy":[16],"samples":[17],"its":[19],"two-dimensional":[20],"projection":[21],"images":[22],"at":[23,163,201],"unknown":[24,100],"random":[25,216],"directions.":[26],"Present":[27],"algorithms":[28,96,154,222],"for":[29,97,240],"finding":[30,98],"an":[31,241],"initial":[32],"3D":[33],"model":[35],"are":[36,155,171,191,205,223],"based":[37,141],"on":[38,142],"\"angular":[40],"reconstitution\"":[41],"method":[42],"in":[43,197,225],"which":[44],"coordinate":[46],"system":[47],"established":[49],"from":[50,66,132],"three":[51,122],"projections,":[52],"and":[53,193,215,219],"orientation":[55],"particle":[58],"giving":[59],"rise":[60],"each":[62],"image":[63],"deduced":[65],"common":[67,77,134,199],"lines":[68,78,200],"among":[69],"images.":[71,89],"However,":[72],"reliable":[74],"detection":[75,167],"difficult":[80],"due":[81],"low":[84,165],"signal-to-noise":[85],"ratio":[86],"In":[90,111],"this":[91],"paper":[92],"we":[93],"describe":[94],"two":[95],"imaging":[101],"directions":[102],"all":[104,161,198],"projections":[105],"by":[106,119],"minimizing":[107],"global":[108],"self-consistency":[109],"errors.":[110],"first":[113],"algorithm,":[114],"minimizer":[116],"obtained":[118],"computing":[120],"largest":[123],"eigenvectors":[124,184],"specially":[127],"designed":[128],"symmetric":[129],"matrix":[130,217],"derived":[131],"lines,":[135],"while":[136],"second":[138],"algorithm":[139],"semidefinite":[143],"programming":[144],"(SDP).":[145],"Compared":[146],"with":[147],"existing":[148],"algorithms,":[149],"advantages":[151],"our":[153],"five-fold:":[156],"first,":[157],"they":[158,170,175,190,204,229],"accurately":[159],"estimate":[160],"orientations":[162],"very":[164],"common-line":[166],"rates;":[168],"second,":[169],"extremely":[172],"fast,":[173],"as":[174],"involve":[176],"only":[177],"computation":[179],"few":[182],"top":[183],"or":[185],"sparse":[187],"SDP;":[188],"third,":[189],"nonsequential":[192],"use":[194],"information":[196,232],"once;":[202],"fourth,":[203],"amenable":[206],"rigorous":[209],"mathematical":[210],"analysis":[211,214],"using":[212],"spectral":[213],"theory;":[218],"finally,":[220],"optimal":[224],"sense":[227],"that":[228],"reach":[230],"theoretic":[233],"Shannon":[234],"bound":[235],"up":[236],"constant":[239],"idealized":[242],"probabilistic":[243],"model.":[244]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":23},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
