{"id":"https://openalex.org/W2107260249","doi":"https://doi.org/10.1109/tsp.2011.2166394","title":"A Novel Sampling Theorem on the Sphere","display_name":"A Novel Sampling Theorem on the Sphere","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W2107260249","doi":"https://doi.org/10.1109/tsp.2011.2166394","mag":"2107260249"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2166394","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2166394","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1110.6298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108816607","display_name":"Jason D. McEwen","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Jason D. McEwen","raw_affiliation_strings":["Institute of Electrical Engineering, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute of Electrical Engineering, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041620227","display_name":"Yves Wiaux","orcid":"https://orcid.org/0000-0002-1658-0121"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Yves Wiaux","raw_affiliation_strings":["Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland","Institute of Electrical Engineering, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]},{"raw_affiliation_string":"Institute of Electrical Engineering, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108816607"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":10.0036,"has_fulltext":false,"cited_by_count":167,"citation_normalized_percentile":{"value":0.98695748,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"59","issue":"12","first_page":"5876","last_page":"5887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9952999949455261,"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/T12603","display_name":"NMR spectroscopy and applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"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/nyquist\u2013shannon-sampling-theorem","display_name":"Nyquist\u2013Shannon sampling theorem","score":0.6816936731338501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.662875771522522},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5597351789474487},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4248262643814087},{"id":"https://openalex.org/keywords/precomputation","display_name":"Precomputation","score":0.4228825867176056},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4022696614265442},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34236323833465576},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3178388476371765},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.2721801996231079},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23860269784927368},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14894968271255493}],"concepts":[{"id":"https://openalex.org/C288623","wikidata":"https://www.wikidata.org/wiki/Q679800","display_name":"Nyquist\u2013Shannon sampling theorem","level":2,"score":0.6816936731338501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.662875771522522},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5597351789474487},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4248262643814087},{"id":"https://openalex.org/C159379195","wikidata":"https://www.wikidata.org/wiki/Q7239568","display_name":"Precomputation","level":3,"score":0.4228825867176056},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4022696614265442},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34236323833465576},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3178388476371765},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2721801996231079},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23860269784927368},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14894968271255493},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2011.2166394","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2166394","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1110.6298","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1110.6298","pdf_url":"https://arxiv.org/pdf/1110.6298","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":null,"raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:165214","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/165214","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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:infoscience.tind.io:165214","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/66613","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1110.6298","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1110.6298","pdf_url":"https://arxiv.org/pdf/1110.6298","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W33851185","https://openalex.org/W621269794","https://openalex.org/W1528387448","https://openalex.org/W1579533523","https://openalex.org/W1601526448","https://openalex.org/W1630643170","https://openalex.org/W1680284398","https://openalex.org/W1838525153","https://openalex.org/W1968059064","https://openalex.org/W1976579441","https://openalex.org/W1977691562","https://openalex.org/W1984376083","https://openalex.org/W1986583619","https://openalex.org/W1986655361","https://openalex.org/W1988954604","https://openalex.org/W1993358632","https://openalex.org/W1995955249","https://openalex.org/W2015251708","https://openalex.org/W2019838186","https://openalex.org/W2021547757","https://openalex.org/W2036203107","https://openalex.org/W2037964341","https://openalex.org/W2045145094","https://openalex.org/W2046193047","https://openalex.org/W2046330884","https://openalex.org/W2052169332","https://openalex.org/W2053289371","https://openalex.org/W2060170052","https://openalex.org/W2070782986","https://openalex.org/W2081237230","https://openalex.org/W2082272630","https://openalex.org/W2096348897","https://openalex.org/W2105867867","https://openalex.org/W2112544671","https://openalex.org/W2118413445","https://openalex.org/W2122775741","https://openalex.org/W2140756509","https://openalex.org/W2145096794","https://openalex.org/W2147875900","https://openalex.org/W2153119069","https://openalex.org/W2160615084","https://openalex.org/W2167127805","https://openalex.org/W2169882521","https://openalex.org/W2296616510","https://openalex.org/W2766596004","https://openalex.org/W2950059253","https://openalex.org/W2963164647","https://openalex.org/W2964220234","https://openalex.org/W3098877636","https://openalex.org/W3099731122","https://openalex.org/W3099955363","https://openalex.org/W3106490840","https://openalex.org/W3122260026","https://openalex.org/W4213223317","https://openalex.org/W4250313187","https://openalex.org/W4250955649","https://openalex.org/W4252598997","https://openalex.org/W4300879736","https://openalex.org/W6636062753","https://openalex.org/W6637439640","https://openalex.org/W6682985916","https://openalex.org/W6684494823","https://openalex.org/W6891651376","https://openalex.org/W6962309597"],"related_works":["https://openalex.org/W126258643","https://openalex.org/W2157769033","https://openalex.org/W2096978683","https://openalex.org/W414359703","https://openalex.org/W2687399516","https://openalex.org/W2543067032","https://openalex.org/W2170398238","https://openalex.org/W3029113864","https://openalex.org/W2020308516","https://openalex.org/W2379572111"],"abstract_inverted_index":{"We":[0,180],"develop":[1],"a":[2,21,39,45],"novel":[3],"sampling":[4,29,57,77,90,107,210],"theorem":[5,30,78,211],"on":[6,47,59,92,168],"the":[7,15,18,32,48,60,83,93,105,128,136,141,169,206,213,220],"sphere":[8,16,49,61,94,170],"and":[9,95,158,165,189,196],"corresponding":[10],"fast":[11,132],"algorithms":[12,113,147,160,186],"by":[13],"associating":[14],"with":[17,140],"torus":[19],"through":[20],"periodic":[22],"extension.":[23],"The":[24,109],"fundamental":[25],"property":[26],"of":[27,34,85,87,102,111,131,184,208,215,222],"any":[28,156,172],"is":[31],"number":[33,84,101],"samples":[35,86,103],"required":[36],"to":[37,162,199],"represent":[38,43],"band-limited":[40,50],"signal.":[41],"To":[42],"exactly":[44],"signal":[46],"at":[51],"<i":[52,63,67,116,120],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[53,64,68,71,117,121,124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L</i>":[54,69,122],",":[55],"all":[56],"theorems":[58,91],"require":[62,155],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">O</i>":[65,118],"(":[66,119],"<sup":[70,123],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[72],")":[73],"samples.":[74],"However,":[75],"our":[76,112,159,182,209],"requires":[79],"less":[80],"than":[81,104],"half":[82],"other":[88],"equiangular":[89],"an":[96],"asymptotically":[97],"identical,":[98],"but":[99],"smaller,":[100],"Gauss-Legendre":[106],"theorem.":[108],"complexity":[110,176],"scale":[114],"as":[115],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sup>":[125],"),":[126],"however,":[127],"continual":[129],"use":[130],"Fourier":[133],"transforms":[134],"reduces":[135],"constant":[137],"prefactor":[138],"associated":[139],"asymptotic":[142],"scaling":[143],"considerably,":[144],"resulting":[145],"in":[146,174,212,219],"that":[148],"are":[149],"fast.":[150],"Furthermore,":[151],"we":[152,204],"do":[153],"not":[154],"precomputation":[157],"apply":[161],"both":[163],"scalar":[164],"spin":[166],"functions":[167],"without":[171],"change":[173],"computational":[175],"or":[177],"computation":[178],"time.":[179],"make":[181],"implementation":[183],"these":[185],"available":[187],"publicly":[188],"perform":[190],"numerical":[191],"experiments":[192],"demonstrating":[193],"their":[194],"speed":[195],"accuracy":[197],"up":[198],"very":[200],"high":[201],"band-limits.":[202],"Finally,":[203],"highlight":[205],"advantages":[207],"context":[214],"potential":[216],"applications,":[217],"notably":[218],"field":[221],"compressive":[223],"sampling.":[224]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}