{"id":"https://openalex.org/W1985492840","doi":"https://doi.org/10.1137/110854497","title":"ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm","display_name":"ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1985492840","doi":"https://doi.org/10.1137/110854497","mag":"1985492840"},"language":"en","primary_location":{"id":"doi:10.1137/110854497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110854497","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"],"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/A5090767423","display_name":"Gitta Kutyniok","orcid":"https://orcid.org/0000-0001-9738-2487"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Gitta Kutyniok","raw_affiliation_strings":["Technische Universitat Berlin"],"affiliations":[{"raw_affiliation_string":"Technische Universitat Berlin","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070271414","display_name":"Morteza Shahram","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Morteza Shahram","raw_affiliation_strings":["Stanford University"],"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073172471","display_name":"Xiaosheng Zhuang","orcid":"https://orcid.org/0000-0001-7238-0143"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Xiaosheng Zhuang","raw_affiliation_strings":["Technische Universitat Berlin"],"affiliations":[{"raw_affiliation_string":"Technische Universitat Berlin","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090767423"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":20.8231,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.99501547,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"5","issue":"4","first_page":"1291","last_page":"1332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9976999759674072,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9635999798774719,"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/shearlet","display_name":"Shearlet","score":0.9634859561920166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6617124080657959},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5606036186218262},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5233922600746155},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4686267673969269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36272382736206055},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.28017204999923706},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22533470392227173},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12101796269416809},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1018812358379364}],"concepts":[{"id":"https://openalex.org/C67795661","wikidata":"https://www.wikidata.org/wiki/Q17018993","display_name":"Shearlet","level":3,"score":0.9634859561920166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6617124080657959},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5606036186218262},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5233922600746155},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4686267673969269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36272382736206055},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.28017204999923706},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22533470392227173},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12101796269416809},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1018812358379364}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110854497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110854497","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":"pmh:oai:CiteSeerX.psu:10.1.1.1027.1218","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1027.1218","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Gitta_Kutyniok/publication/51910367_ShearLab_A_Rational_Design_of_a_Digital_Parabolic_Scaling_Algorithm/links/0912f50e4844ef3c13000000.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.231.4828","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.4828","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.shearlet.org/papers/ShearLab.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2160137948","display_name":null,"funder_award_id":"KU 1446/14","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3127212197","display_name":null,"funder_award_id":"SPP-1324","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6537435729","display_name":null,"funder_award_id":"Heisenberg","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8965197529","display_name":null,"funder_award_id":"SPP-1324 KU 1446/13","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320308380","display_name":"Yale University","ror":"https://ror.org/03v76x132"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W55358352","https://openalex.org/W1541049108","https://openalex.org/W1762506961","https://openalex.org/W1977642227","https://openalex.org/W1979116456","https://openalex.org/W1990805796","https://openalex.org/W2030620341","https://openalex.org/W2035871342","https://openalex.org/W2063786008","https://openalex.org/W2066462711","https://openalex.org/W2069912449","https://openalex.org/W2072476274","https://openalex.org/W2078498319","https://openalex.org/W2085744431","https://openalex.org/W2097061348","https://openalex.org/W2115528090","https://openalex.org/W2117853853","https://openalex.org/W2117881455","https://openalex.org/W2119337797","https://openalex.org/W2122735658","https://openalex.org/W2137155471","https://openalex.org/W2138923206","https://openalex.org/W2154625249","https://openalex.org/W2170860899","https://openalex.org/W2319308948","https://openalex.org/W2962880471","https://openalex.org/W2963851978","https://openalex.org/W4210381520"],"related_works":["https://openalex.org/W2475220750","https://openalex.org/W2016759271","https://openalex.org/W2072476274","https://openalex.org/W2949924583","https://openalex.org/W2018897187","https://openalex.org/W4299617494","https://openalex.org/W1541049108","https://openalex.org/W2145495275","https://openalex.org/W2950003032","https://openalex.org/W1496339867"],"abstract_inverted_index":{"Multivariate":[0],"problems":[1],"are":[2],"typically":[3],"governed":[4],"by":[5,125],"anisotropic":[6],"features":[7,34],"such":[8,33,195],"as":[9,184,186],"edges":[10],"in":[11,50,66,172],"images.":[12],"A":[13],"common":[14],"bracket":[15],"of":[16,18,32,38,74,91,103,114,128,134,147,194],"most":[17],"the":[19,36,45,67,72,75,93,101,107,129,138,148,182,201],"various":[20,164],"directional":[21,189],"representation":[22],"systems":[23],"which":[24,62],"have":[25],"been":[26],"proposed":[27],"to":[28,143,176],"deliver":[29],"sparse":[30],"approximations":[31],"is":[35,44,53,63,71,158,197],"utilization":[37,102],"parabolic":[39,115,169],"scaling.":[40],"One":[41],"prominent":[42],"example":[43],"shearlet":[46,60,77,85,149,203],"system.":[47],"Our":[48],"objective":[49],"this":[51],"paper":[52],"threefold:":[54],"We":[55,118],"first":[56],"develop":[57],"a":[58,88,144],"digital":[59,96,112,145,168,202],"theory":[61,78,86],"rationally":[64],"designed":[65],"sense":[68],"that":[69,84],"it":[70],"digitization":[73],"existing":[76],"for":[79,111,137,167,200],"continuous":[80],"data.":[81],"This":[82,141],"implies":[83],"provides":[87],"unified":[89],"treatment":[90],"both":[92],"continuum":[94],"and":[95,106,179],"realms.":[97],"Second,":[98],"we":[99,162],"analyze":[100],"pseudo-polar":[104,108,122,130],"grids":[105],"Fourier":[109,123],"transform":[110,124,190],"implementations":[113],"scaling":[116,170],"algorithms.":[117],"derive":[119],"an":[120,151],"isometric":[121],"careful":[126],"weighting":[127],"grid,":[131],"allowing":[132,174],"exploitation":[133],"its":[135],"adjoint":[136],"inverse":[139],"transform.":[140,204],"leads":[142],"implementation":[146,183],"transform;":[150],"accompanying":[152],"MATLAB":[153],"toolbox":[154],"called":[155],"ShearLab":[156],"(www.ShearLab.org)":[157],"provided.":[159],"And,":[160],"third,":[161],"introduce":[163],"quantitative":[165],"measures":[166,196],"algorithms":[171],"general,":[173],"one":[175],"tune":[177],"parameters":[178],"objectively":[180],"improve":[181],"well":[185],"compare":[187],"different":[188],"implementations.":[191],"The":[192],"usefulness":[193],"exemplarily":[198],"demonstrated":[199]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}