{"id":"https://openalex.org/W2766477323","doi":"https://doi.org/10.1137/17m1153509","title":"Structural Variability from Noisy Tomographic Projections","display_name":"Structural Variability from Noisy Tomographic Projections","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2766477323","doi":"https://doi.org/10.1137/17m1153509","mag":"2766477323","pmid":"https://pubmed.ncbi.nlm.nih.gov/30555617"},"language":"en","primary_location":{"id":"doi:10.1137/17m1153509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1153509","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":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.09791","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043290570","display_name":"Joakim And\u00e9n","orcid":"https://orcid.org/0000-0002-3377-813X"},"institutions":[{"id":"https://openalex.org/I4210153546","display_name":"Flatiron Health (United States)","ror":"https://ror.org/0508h6p74","country_code":"US","type":"company","lineage":["https://openalex.org/I4210153546"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joakim And\u00e9n","raw_affiliation_strings":["Center for Computational Biology, Flatiron Institute, New York, NY 10100"],"affiliations":[{"raw_affiliation_string":"Center for Computational Biology, Flatiron Institute, New York, NY 10100","institution_ids":["https://openalex.org/I4210153546"]}]},{"author_position":"last","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":false,"raw_author_name":"Amit Singer","raw_affiliation_strings":["Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043290570"],"corresponding_institution_ids":["https://openalex.org/I4210153546"],"apc_list":null,"apc_paid":null,"fwci":0.1902,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72196262,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"2","first_page":"1441","last_page":"1492"},"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":0.9987000226974487,"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":0.9987000226974487,"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":0.9972000122070312,"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/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9538999795913696,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6262819766998291},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.604127049446106},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5741205811500549},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5593871474266052},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5580407381057739},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.523657500743866},{"id":"https://openalex.org/keywords/deconvolution","display_name":"Deconvolution","score":0.49814486503601074},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.49363625049591064},{"id":"https://openalex.org/keywords/mat\u00e9rn-covariance-function","display_name":"Mat\u00e9rn covariance function","score":0.4397442936897278},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.42980048060417175},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4256754219532013},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.30724209547042847},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19689041376113892},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18598371744155884},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10409331321716309}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6262819766998291},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.604127049446106},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5741205811500549},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5593871474266052},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5580407381057739},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.523657500743866},{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.49814486503601074},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.49363625049591064},{"id":"https://openalex.org/C118006245","wikidata":"https://www.wikidata.org/wiki/Q6792079","display_name":"Mat\u00e9rn covariance function","level":5,"score":0.4397442936897278},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.42980048060417175},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4256754219532013},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.30724209547042847},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19689041376113892},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18598371744155884},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10409331321716309},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/17m1153509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1153509","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:30555617","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30555617","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:arXiv.org:1710.09791","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.09791","pdf_url":"https://arxiv.org/pdf/1710.09791","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:europepmc.org:5262910","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6294454","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"},{"id":"doi:10.48550/arxiv.1710.09791","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.09791","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2766477323","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.09791","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.09791","pdf_url":"https://arxiv.org/pdf/1710.09791","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":85,"referenced_works":["https://openalex.org/W36187607","https://openalex.org/W93530381","https://openalex.org/W575681570","https://openalex.org/W1483313280","https://openalex.org/W1483804921","https://openalex.org/W1492556495","https://openalex.org/W1506342804","https://openalex.org/W1520752838","https://openalex.org/W1533471646","https://openalex.org/W1548938959","https://openalex.org/W1568854817","https://openalex.org/W1576783654","https://openalex.org/W1623890683","https://openalex.org/W1967374108","https://openalex.org/W1970377488","https://openalex.org/W1975696503","https://openalex.org/W1978885539","https://openalex.org/W1982584811","https://openalex.org/W2001923477","https://openalex.org/W2005041367","https://openalex.org/W2005240547","https://openalex.org/W2006025109","https://openalex.org/W2010122118","https://openalex.org/W2011665065","https://openalex.org/W2012300893","https://openalex.org/W2016982898","https://openalex.org/W2017508876","https://openalex.org/W2021703585","https://openalex.org/W2036823849","https://openalex.org/W2040957249","https://openalex.org/W2044098317","https://openalex.org/W2047902460","https://openalex.org/W2048826637","https://openalex.org/W2049633694","https://openalex.org/W2051925784","https://openalex.org/W2053860607","https://openalex.org/W2057602562","https://openalex.org/W2058583833","https://openalex.org/W2060581589","https://openalex.org/W2061171222","https://openalex.org/W2072834874","https://openalex.org/W2073949924","https://openalex.org/W2080097309","https://openalex.org/W2092709807","https://openalex.org/W2104234755","https://openalex.org/W2105367101","https://openalex.org/W2106005123","https://openalex.org/W2115755118","https://openalex.org/W2117948104","https://openalex.org/W2121752514","https://openalex.org/W2121947440","https://openalex.org/W2128801186","https://openalex.org/W2133307020","https://openalex.org/W2139916860","https://openalex.org/W2142158597","https://openalex.org/W2143962756","https://openalex.org/W2147001810","https://openalex.org/W2148575499","https://openalex.org/W2150593711","https://openalex.org/W2150790075","https://openalex.org/W2150938882","https://openalex.org/W2160880244","https://openalex.org/W2164659462","https://openalex.org/W2167034439","https://openalex.org/W2316564661","https://openalex.org/W2498179566","https://openalex.org/W2569750427","https://openalex.org/W2574455081","https://openalex.org/W2587625522","https://openalex.org/W2588224366","https://openalex.org/W2592692890","https://openalex.org/W2606074844","https://openalex.org/W2609504638","https://openalex.org/W2783817513","https://openalex.org/W2950967305","https://openalex.org/W2952274186","https://openalex.org/W2962946304","https://openalex.org/W2963099215","https://openalex.org/W2963653055","https://openalex.org/W2963669613","https://openalex.org/W2963927955","https://openalex.org/W3007034419","https://openalex.org/W4213367101","https://openalex.org/W4233363368","https://openalex.org/W4250038851"],"related_works":["https://openalex.org/W1976695151","https://openalex.org/W2074370150","https://openalex.org/W2109035534","https://openalex.org/W2170850527","https://openalex.org/W2520625856","https://openalex.org/W2121193959","https://openalex.org/W3106305553","https://openalex.org/W1996780521","https://openalex.org/W2903399336","https://openalex.org/W1568304908","https://openalex.org/W2566587511","https://openalex.org/W2963390701","https://openalex.org/W2902086637","https://openalex.org/W3102810310","https://openalex.org/W3037785859","https://openalex.org/W2019606227","https://openalex.org/W3198792048","https://openalex.org/W3200068506","https://openalex.org/W1977599029","https://openalex.org/W2807773213"],"abstract_inverted_index":{"In":[0],"cryo-electron":[1],"microscopy,":[2],"the":[3,60,64,68,73,124,131,138,141,158,170,179,200,255,258],"three-dimensional":[4],"(3D)":[5],"electric":[6],"potentials":[7,29],"of":[8,11,35,67,75,92,178,203,257,264],"an":[9,98,163,251],"ensemble":[10],"molecules":[12],"are":[13,144],"projected":[14],"along":[15],"arbitrary":[16],"viewing":[17],"directions":[18],"to":[19,58,146,193,236],"yield":[20],"noisy":[21,183],"two-dimensional":[22],"images.":[23],"The":[24,167],"volume":[25],"maps":[26],"representing":[27],"these":[28],"typically":[30],"exhibit":[31],"a":[32,80,85,147,214],"great":[33],"deal":[34],"structural":[36,265],"variability,":[37],"which":[38],"is":[39,50,128,154,169],"described":[40],"by":[41,157,199],"their":[42],"3D":[43,180],"covariance":[44,48,77,103,181,209],"matrix.":[45],"Typically,":[46],"this":[47,76,102],"matrix":[49,78,210],"approximately":[51],"low":[52],"rank":[53],"and":[54,231],"can":[55],"be":[56],"used":[57],"cluster":[59],"volumes":[61,249],"or":[62],"estimate":[63],"intrinsic":[65],"geometry":[66],"conformation":[69],"space.":[70],"We":[71,224,243],"formulate":[72],"estimation":[74,177],"as":[79],"linear":[81],"inverse":[82],"problem,":[83],"yielding":[84],"consistent":[86,176],"least-squares":[87],"estimator.":[88],"For":[89],"<i>n</i>":[90],"images":[91],"size":[93],"<i>N</i>-by-<i>N</i>":[94],"pixels,":[95],"we":[96,212],"propose":[97],"algorithm":[99,174,260],"for":[100,175,207,261],"calculating":[101],"estimator":[104],"with":[105,162,191],"computational":[106],"complexity":[107],"<mml:math":[108],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>O</mml:mi>":[109],"<mml:mo>(</mml:mo>":[110],"<mml:mi>n</mml:mi>":[111],"<mml:msup><mml:mi>N</mml:mi>":[112,116],"<mml:mn>4</mml:mn></mml:msup>":[113],"<mml:mo>+</mml:mo>":[114],"<mml:msqrt><mml:mi>\u03ba</mml:mi></mml:msqrt>":[115],"<mml:mn>6</mml:mn></mml:msup>":[117],"<mml:mo>log</mml:mo>":[118],"<mml:mi>N</mml:mi>":[119],"<mml:mo>)</mml:mo></mml:mrow>":[120],"</mml:math>":[121],",":[122],"where":[123],"condition":[125],"number":[126],"<i>\u03ba</i>":[127],"empirically":[129],"in":[130,150,189,239,250],"range":[132],"10-200.":[133],"Its":[134],"efficiency":[135],"relies":[136],"on":[137,228,247],"observation":[139],"that":[140,217],"normal":[142],"equations":[143],"equivalent":[145],"deconvolution":[148],"problem":[149],"six":[151],"dimensions.":[152],"This":[153],"then":[155],"solved":[156],"conjugate":[159],"gradient":[160],"method":[161],"appropriate":[164],"circulant":[165],"preconditioner.":[166],"result":[168],"first":[171],"computationally":[172],"efficient":[173],"from":[182],"projections.":[184],"It":[185],"also":[186,244],"compares":[187],"favorably":[188],"runtime":[190],"respect":[192],"previously":[194],"proposed":[195,259],"nonconsistent":[196],"estimators.":[197],"Motivated":[198],"recent":[201],"success":[202],"eigenvalue":[204],"shrinkage":[205,215],"procedures":[206],"high-dimensional":[208],"estimation,":[211],"incorporate":[213],"procedure":[216],"improves":[218],"accuracy":[219],"at":[220],"lower":[221],"signal-to-noise":[222],"ratios.":[223],"evaluate":[225],"our":[226],"methods":[227,238],"simulated":[229],"datasets":[230],"achieve":[232],"classification":[233],"results":[234,246],"comparable":[235],"state-of-the-art":[237],"shorter":[240],"running":[241],"time.":[242],"present":[245],"clustering":[248],"experimental":[252],"dataset,":[253],"illustrating":[254],"power":[256],"practical":[262],"determination":[263],"variability.":[266]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
