{"id":"https://openalex.org/W2085744431","doi":"https://doi.org/10.1137/060650283","title":"A Framework for Discrete Integral Transformations I\u2014The Pseudopolar Fourier Transform","display_name":"A Framework for Discrete Integral Transformations I\u2014The Pseudopolar Fourier Transform","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2085744431","doi":"https://doi.org/10.1137/060650283","mag":"2085744431"},"language":"en","primary_location":{"id":"doi:10.1137/060650283","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060650283","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-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/A5080836593","display_name":"Amir Averbuch","orcid":"https://orcid.org/0000-0001-8177-235X"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Averbuch","raw_affiliation_strings":["Yale University  ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yale University  ;","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110436903","display_name":"Ronald R. Coifman","orcid":"https://orcid.org/0000-0001-7336-7784"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. R. Coifman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065355421","display_name":"David L. Donoho","orcid":"https://orcid.org/0000-0003-1830-710X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. L. Donoho","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111602084","display_name":"M. Israeli","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Israeli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"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":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.1,"has_fulltext":false,"cited_by_count":102,"citation_normalized_percentile":{"value":0.97247057,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"30","issue":"2","first_page":"764","last_page":"784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9872999787330627,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6926293969154358},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6150632500648499},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5915971994400024},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5380430221557617},{"id":"https://openalex.org/keywords/discrete-time-fourier-transform","display_name":"Discrete-time Fourier transform","score":0.5355755090713501},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.49337974190711975},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4811040759086609},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.470664381980896},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.45831578969955444},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38156449794769287},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.32870179414749146},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3234216570854187},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2952670454978943}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6926293969154358},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6150632500648499},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5915971994400024},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5380430221557617},{"id":"https://openalex.org/C122444316","wikidata":"https://www.wikidata.org/wiki/Q1440048","display_name":"Discrete-time Fourier transform","level":5,"score":0.5355755090713501},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.49337974190711975},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4811040759086609},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.470664381980896},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.45831578969955444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38156449794769287},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.32870179414749146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3234216570854187},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2952670454978943}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/060650283","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060650283","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.3073","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.3073","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.yale.edu/homes/ys264/preprints/2DradonII_v9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.409.2552","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.2552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~amir1/PS/2DradonII_v11.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.409.5814","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.5814","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~amir1/PS/065030.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.409.6275","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.6275","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~amir1/PS/2DradonII_v5.pdf","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":33,"referenced_works":["https://openalex.org/W1515474230","https://openalex.org/W1535724155","https://openalex.org/W1560263223","https://openalex.org/W1897964739","https://openalex.org/W1969011622","https://openalex.org/W1979261054","https://openalex.org/W1979887666","https://openalex.org/W1984869715","https://openalex.org/W1987733917","https://openalex.org/W1988484725","https://openalex.org/W1993029803","https://openalex.org/W1996777044","https://openalex.org/W1998152471","https://openalex.org/W1998252779","https://openalex.org/W2010122118","https://openalex.org/W2012300893","https://openalex.org/W2020067944","https://openalex.org/W2058583833","https://openalex.org/W2061171222","https://openalex.org/W2078498319","https://openalex.org/W2087772495","https://openalex.org/W2096000002","https://openalex.org/W2103030298","https://openalex.org/W2115528090","https://openalex.org/W2119782970","https://openalex.org/W2132680427","https://openalex.org/W2152035672","https://openalex.org/W2153177617","https://openalex.org/W2154625249","https://openalex.org/W2162985161","https://openalex.org/W2505748338","https://openalex.org/W2798909945","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2154898175","https://openalex.org/W3166675296","https://openalex.org/W4353087863","https://openalex.org/W4295678671","https://openalex.org/W3141389362","https://openalex.org/W4251928798","https://openalex.org/W2409547638","https://openalex.org/W2095636570","https://openalex.org/W2073363564","https://openalex.org/W2374649290"],"abstract_inverted_index":{"Abstract.":[0],"Although":[1],"naturally":[2],"at":[3,68],"the":[4,20,88,105,127,132,144,149],"heart":[5],"of":[6,45,61,99,129],"many":[7,15],"fundamental":[8],"physical":[9],"computations,":[10],"and":[11,38,110],"potentially":[12],"useful":[13],"in":[14,101,131],"important":[16],"image":[17],"processing":[18],"tasks,":[19],"Radon":[21,48,146],"transform":[22,106,147,152],"lacks":[23],"a":[24,43,77,96,114,138,172],"coherent":[25],"discrete":[26,31,47,52,139,145,168],"definition":[27,81,166],"for":[28,50,103,167],"two-dimensional":[29],"(2D)":[30],"images":[32,169],"which":[33,54,104,142],"is":[34,55,82,107,126],"algebraically":[35],"exact,":[36],"invertible,":[37],"rapidly":[39,108],"computable.":[40],"We":[41,112],"define":[42],"notion":[44],"2D":[46,51],"transforms":[49],"images,":[53],"based":[56],"on":[57,76],"summation":[58,89],"along":[59],"lines":[60,100],"absolute":[62],"slope":[63],"less":[64],"than":[65],"1.":[66],"Values":[67],"nongrid":[69],"locations":[70],"are":[71],"defined":[72],"using":[73,117],"trigonometric":[74],"interpolation":[75],"zero-padded":[78],"grid.":[79],"Our":[80,93,165],"shown":[83],"to":[84,171],"be":[85],"geometrically":[86],"faithful:":[87],"avoids":[90],"wrap-around":[91],"effects.":[92],"proposal":[94],"uses":[95],"special":[97],"collection":[98],"R2":[102],"computable":[109],"invertible.":[111],"describe":[113],"fast":[115,135],"algorithm":[116,136],"O(N":[118],"log":[119],"N)":[120],"operations,":[121],"where":[122],"N":[123],"=":[124],"n2":[125],"number":[128],"pixels":[130],"image.":[133],"The":[134],"exploits":[137],"projection-slice":[140],"theorem,":[141],"associates":[143],"with":[148,176],"pseudopolar":[150],"Fourier":[151],"[A.":[153],"Averbuch":[154],"et":[155],"al.,":[156],"SIAM":[157],"J.":[158],"Sci.":[159],"Comput.,":[160],"30":[161],"(2008),":[162],"pp.":[163],"764\u2013784].":[164],"converges":[170],"natural":[173],"continuous":[174],"counterpart":[175],"increasing":[177],"refinement.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":14}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}