{"id":"https://openalex.org/W2029487796","doi":"https://doi.org/10.1142/s021969130800229x","title":"THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM","display_name":"THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W2029487796","doi":"https://doi.org/10.1142/s021969130800229x","mag":"2029487796"},"language":"en","primary_location":{"id":"doi:10.1142/s021969130800229x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969130800229x","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","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/A5047150999","display_name":"Stephan Dahlke","orcid":"https://orcid.org/0000-0003-0168-7257"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"STEPHAN DAHLKE","raw_affiliation_strings":["Philipps-Universit\u00e4t Marburg, FB12 Mathematik und Informatik, Hans-Meerwein Stra\u00dfe, Lahnberge, 35032 Marburg, Germany"],"affiliations":[{"raw_affiliation_string":"Philipps-Universit\u00e4t Marburg, FB12 Mathematik und Informatik, Hans-Meerwein Stra\u00dfe, Lahnberge, 35032 Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090767423","display_name":"Gitta Kutyniok","orcid":"https://orcid.org/0000-0001-9738-2487"},"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":"GITTA KUTYNIOK","raw_affiliation_strings":["Program in Applied and Computational Mathematics, Princeton University, Washington Road, Fine Hall, Princeton, NJ 08544-1000, USA"],"affiliations":[{"raw_affiliation_string":"Program in Applied and Computational Mathematics, Princeton University, Washington Road, Fine Hall, Princeton, NJ 08544-1000, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018483872","display_name":"Peter Maa\u00df","orcid":"https://orcid.org/0000-0003-1448-8345"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"PETER MAASS","raw_affiliation_strings":["Fachbereich 3, Universit\u00e4t Bremen, Postfach 33 04 40, 28334 Bremen, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich 3, Universit\u00e4t Bremen, Postfach 33 04 40, 28334 Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047049214","display_name":"Chen Sagiv","orcid":null},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"CHEN SAGIV","raw_affiliation_strings":["Fachbereich 3, Universit\u00e4t Bremen, Postfach 33 04 40, 28334 Bremen, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich 3, Universit\u00e4t Bremen, Postfach 33 04 40, 28334 Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035247857","display_name":"Hans\u2010Georg Stark","orcid":null},"institutions":[{"id":"https://openalex.org/I4210158205","display_name":"Aschaffenburg University of Applied Sciences","ror":"https://ror.org/04sms9203","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210158205"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"HANS-GEORG STARK","raw_affiliation_strings":["Fachhochschule Aschaffenburg, Mathematik/Informatik/Technomathematik, W\u00fcrzburger Str. 45, 63743 Aschaffenburg, Germany"],"affiliations":[{"raw_affiliation_string":"Fachhochschule Aschaffenburg, Mathematik/Informatik/Technomathematik, W\u00fcrzburger Str. 45, 63743 Aschaffenburg, Germany","institution_ids":["https://openalex.org/I4210158205"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014085627","display_name":"Gerd Teschke","orcid":"https://orcid.org/0000-0002-6912-690X"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"GERD TESCHKE","raw_affiliation_strings":["Research Group Inverse Problems in Science and Technology, Konrad-Zuse-Zentrum f\u00fcr Informationstechnik Berlin (ZIB), Takustr. 7, 14195 Berlin-Dahlem, Germany"],"affiliations":[{"raw_affiliation_string":"Research Group Inverse Problems in Science and Technology, Konrad-Zuse-Zentrum f\u00fcr Informationstechnik Berlin (ZIB), Takustr. 7, 14195 Berlin-Dahlem, Germany","institution_ids":["https://openalex.org/I195893171"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5047150999"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":null,"apc_paid":null,"fwci":7.7259,"has_fulltext":false,"cited_by_count":146,"citation_normalized_percentile":{"value":0.97595526,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"06","issue":"02","first_page":"157","last_page":"181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9991000294685364,"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":0.9991000294685364,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9955999851226807,"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":0.9955999851226807,"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/shearlet","display_name":"Shearlet","score":0.9894968271255493},{"id":"https://openalex.org/keywords/curvelet","display_name":"Curvelet","score":0.7072594165802002},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.574274480342865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5369000434875488},{"id":"https://openalex.org/keywords/continuous-wavelet-transform","display_name":"Continuous wavelet transform","score":0.5147805213928223},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.4839332699775696},{"id":"https://openalex.org/keywords/uncertainty-principle","display_name":"Uncertainty principle","score":0.4445821940898895},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4247640371322632},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.4182230234146118},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35604554414749146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3559226989746094},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.2508072257041931},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24208348989486694}],"concepts":[{"id":"https://openalex.org/C67795661","wikidata":"https://www.wikidata.org/wiki/Q17018993","display_name":"Shearlet","level":3,"score":0.9894968271255493},{"id":"https://openalex.org/C131720326","wikidata":"https://www.wikidata.org/wiki/Q5196075","display_name":"Curvelet","level":4,"score":0.7072594165802002},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.574274480342865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5369000434875488},{"id":"https://openalex.org/C95722684","wikidata":"https://www.wikidata.org/wiki/Q2622756","display_name":"Continuous wavelet transform","level":5,"score":0.5147805213928223},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.4839332699775696},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.4445821940898895},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4247640371322632},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.4182230234146118},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35604554414749146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3559226989746094},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.2508072257041931},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24208348989486694},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021969130800229x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969130800229x","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W32859232","https://openalex.org/W627728979","https://openalex.org/W1485280399","https://openalex.org/W1504272734","https://openalex.org/W1516049615","https://openalex.org/W1654995442","https://openalex.org/W1800418436","https://openalex.org/W1868105354","https://openalex.org/W1990805796","https://openalex.org/W1996021349","https://openalex.org/W2005614736","https://openalex.org/W2010527846","https://openalex.org/W2036854047","https://openalex.org/W2066462711","https://openalex.org/W2073996439","https://openalex.org/W2081214999","https://openalex.org/W2108472799","https://openalex.org/W2116863932","https://openalex.org/W2117853853","https://openalex.org/W2121690517","https://openalex.org/W2129276048","https://openalex.org/W2137155471","https://openalex.org/W2319308948","https://openalex.org/W2567165719","https://openalex.org/W2973818247","https://openalex.org/W4229923956","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4205674299","https://openalex.org/W2168226778","https://openalex.org/W2296210702","https://openalex.org/W2128709529","https://openalex.org/W2210038017","https://openalex.org/W1994254883","https://openalex.org/W1674776290","https://openalex.org/W3037462281","https://openalex.org/W2265646695","https://openalex.org/W2025423598"],"abstract_inverted_index":{"Finding":[0],"optimal":[1,75],"representations":[2],"of":[3,16,33,77,80,137,152],"signals":[4],"in":[5,8,30,44,120],"higher":[6],"dimensions,":[7],"particular":[9],"directional":[10,28],"representations,":[11],"is":[12,92],"currently":[13],"the":[14,20,31,35,45,61,78,81,101,107,116,129,134,138,153,166,169,179,182],"subject":[15],"intensive":[17],"research.":[18],"Since":[19],"classical":[21],"wavelet":[22],"transform":[23,91],"does":[24],"not":[25],"provide":[26],"precise":[27],"information":[29],"sense":[32],"resolving":[34],"wavefront":[36],"set,":[37],"several":[38],"new":[39],"representation":[40,98],"systems":[41],"were":[42],"proposed":[43],"past,":[46],"including":[47],"ridgelets,":[48],"curvelets":[49],"and,":[50],"more":[51],"recently,":[52],"Shearlets.":[53],"In":[54],"this":[55,90],"paper":[56],"we":[57,66,86,163],"study":[58,164],"and":[59,105,143,181],"visualize":[60],"continuous":[62],"Shearlet":[63,71,103,125,139],"transform.":[64,83],"Moreover,":[65,162],"aim":[67],"at":[68],"deriving":[69],"mother":[70,124],"functions":[72,126],"which":[73],"ensure":[74,150],"accuracy":[76],"parameters":[79],"associated":[82,93,108],"For":[84],"this,":[85],"first":[87],"show":[88],"that":[89,127],"with":[94],"a":[95,174],"unitary":[96],"group":[97,104],"coming":[99],"from":[100],"so-called":[102],"compute":[106],"admissibility":[109,170,183],"condition.":[110],"This":[111],"enables":[112],"us":[113],"to":[114,122,149,176],"employ":[115],"general":[117],"uncertainty":[118,130],"principle":[119],"order":[121],"derive":[123],"minimize":[128],"relations":[131],"derived":[132,154],"for":[133],"infinitesimal":[135],"generators":[136],"group:":[140],"scaling,":[141],"shear":[142],"translations.":[144],"We":[145],"further":[146],"discuss":[147],"methods":[148],"square-integrability":[151],"minimizers":[155,167],"by":[156],"considering":[157],"weighted":[158],"L":[159],"2":[160],"-spaces.":[161],"whether":[165],"satisfy":[168],"condition,":[171],"thereby":[172],"proposing":[173],"method":[175],"balance":[177],"between":[178],"minimizing":[180],"property.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":13}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
