{"id":"https://openalex.org/W1983697382","doi":"https://doi.org/10.1137/s0036141096309617","title":"Angular Channels in a Multidimensional Wavelet Transform","display_name":"Angular Channels in a Multidimensional Wavelet Transform","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1983697382","doi":"https://doi.org/10.1137/s0036141096309617","mag":"1983697382"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141096309617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141096309617","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5078532077","display_name":"Eric Clarkson","orcid":"https://orcid.org/0000-0003-3867-4070"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Eric Clarkson","raw_affiliation_strings":["Medical Imaging"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Medical Imaging","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5078532077"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12234451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"1","first_page":"80","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998000264167786,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9947999715805054,"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":0.9846000075340271,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8039044141769409},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7267311811447144},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.7257904410362244},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.7149906158447266},{"id":"https://openalex.org/keywords/harmonic-wavelet-transform","display_name":"Harmonic wavelet transform","score":0.7032878398895264},{"id":"https://openalex.org/keywords/stationary-wavelet-transform","display_name":"Stationary wavelet transform","score":0.5661438703536987},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5332303643226624},{"id":"https://openalex.org/keywords/second-generation-wavelet-transform","display_name":"Second-generation wavelet transform","score":0.5164216160774231},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.51639324426651},{"id":"https://openalex.org/keywords/lifting-scheme","display_name":"Lifting scheme","score":0.4687892198562622},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4287932217121124},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3898046612739563},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11507090926170349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11163541674613953}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8039044141769409},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7267311811447144},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.7257904410362244},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.7149906158447266},{"id":"https://openalex.org/C1109138","wikidata":"https://www.wikidata.org/wiki/Q3280930","display_name":"Harmonic wavelet transform","level":5,"score":0.7032878398895264},{"id":"https://openalex.org/C73339587","wikidata":"https://www.wikidata.org/wiki/Q1375942","display_name":"Stationary wavelet transform","level":5,"score":0.5661438703536987},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5332303643226624},{"id":"https://openalex.org/C111350171","wikidata":"https://www.wikidata.org/wiki/Q7443700","display_name":"Second-generation wavelet transform","level":5,"score":0.5164216160774231},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.51639324426651},{"id":"https://openalex.org/C199550912","wikidata":"https://www.wikidata.org/wiki/Q3238415","display_name":"Lifting scheme","level":5,"score":0.4687892198562622},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4287932217121124},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3898046612739563},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11507090926170349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11163541674613953}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036141096309617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141096309617","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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":17,"referenced_works":["https://openalex.org/W1542897689","https://openalex.org/W1963910623","https://openalex.org/W1998630480","https://openalex.org/W2002716691","https://openalex.org/W2005614736","https://openalex.org/W2014757225","https://openalex.org/W2016657207","https://openalex.org/W2020651755","https://openalex.org/W2058399510","https://openalex.org/W2071806922","https://openalex.org/W2074428329","https://openalex.org/W2096684483","https://openalex.org/W2106341174","https://openalex.org/W2126777570","https://openalex.org/W2151035292","https://openalex.org/W2151996103","https://openalex.org/W2166982406"],"related_works":["https://openalex.org/W1588899229","https://openalex.org/W1976022598","https://openalex.org/W2085792030","https://openalex.org/W2144408025","https://openalex.org/W1506615375","https://openalex.org/W2391053410","https://openalex.org/W2205192157","https://openalex.org/W1967182499","https://openalex.org/W2156522110","https://openalex.org/W4321517526"],"abstract_inverted_index":{"Given":[0],"a":[1],"subgroup":[2],"S":[3,13],"of":[4,12,32,40,67,74,88,104,107,120,127,147,151],"GL(n),":[5],"let":[6],"G":[7,33],"be":[8,100],"the":[9,30,41,57,61,81,118,143,148,152],"semidirect":[10],"product":[11],"with":[14],"${\\Bbb":[15],"R}^n.$":[16],"The":[17,37,72,137],"wavelet":[18,42,62,76,82,108,123,129,153],"transform":[19,43,83,124,150,154],"is":[20,63,78,84,133,155],"defined":[21],"for":[22,60,117,135],"functions":[23],"in":[24,52,65,86,102,125],"$L^2\\left({\\Bbb":[25],"R}^n\\right)":[26,96],"$":[27,97],"by":[28],"using":[29],"action":[31],"on":[34,92],"this":[35,53],"space.":[36],"standard":[38],"properties":[39],"and":[44,49,80,112,142],"its":[45],"inverse":[46],"are":[47,115],"quickly":[48],"easily":[50],"derived":[51],"formalism.":[54],"In":[55],"particular,":[56],"admissibility":[58],"condition":[59],"expressed":[64],"terms":[66,87,103,126],"an":[68,121],"integral":[69],"over":[70],"S.":[71],"notion":[73],"orthogonal":[75],"channels":[77,141],"defined,":[79],"decomposed":[85],"them.":[89],"Other":[90],"operators":[91],"$%":[93],"L^2\\left(":[94],"{\\Bbb":[95],"can":[98],"also":[99,156],"analyzed":[101],"their":[105],"mixing":[106],"channels.":[109,130],"For":[110],"n=2":[111],"n=3,":[113],"details":[114],"given":[116],"expansion":[119],"arbitrary":[122],"angular":[128,140],"An":[131],"example":[132],"provided":[134],"n=2.":[136],"correspondence":[138],"between":[139],"spherical":[144],"harmonic":[145],"decomposition":[146],"Fourier":[149],"outlined.":[157]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
