{"id":"https://openalex.org/W2987953629","doi":"https://doi.org/10.1142/s0219691320500095","title":"Multiscaling frame multiresolution analysis and associated wavelet frames","display_name":"Multiscaling frame multiresolution analysis and associated wavelet frames","publication_year":2019,"publication_date":"2019-11-15","ids":{"openalex":"https://openalex.org/W2987953629","doi":"https://doi.org/10.1142/s0219691320500095","mag":"2987953629"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691320500095","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691320500095","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/A5044080622","display_name":"Xiaojiang Yu","orcid":"https://orcid.org/0000-0003-3602-1797"},"institutions":[{"id":"https://openalex.org/I198091727","display_name":"Tiangong University","ror":"https://ror.org/00xsr9m91","country_code":"CN","type":"education","lineage":["https://openalex.org/I198091727"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaojiang Yu","raw_affiliation_strings":["Department of Data Science and Big Data Technology, Tiangong University, Tianjin 300387, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-3602-1797","affiliations":[{"raw_affiliation_string":"Department of Data Science and Big Data Technology, Tiangong University, Tianjin 300387, P. R. China","institution_ids":["https://openalex.org/I198091727"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044080622"],"corresponding_institution_ids":["https://openalex.org/I198091727"],"apc_list":null,"apc_paid":null,"fwci":0.3312,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.56071693,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"03","first_page":"2050009","last_page":"2050009"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9957000017166138,"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":0.9721999764442444,"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/parsevals-theorem","display_name":"Parseval's theorem","score":0.8942183256149292},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7010469436645508},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.562872588634491},{"id":"https://openalex.org/keywords/multiresolution-analysis","display_name":"Multiresolution analysis","score":0.5527082681655884},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5449870228767395},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5240352749824524},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.45755043625831604},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4196814000606537},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4050019085407257},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39269453287124634},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.3890443444252014},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36736738681793213},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3284938931465149},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.2872140109539032},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26893019676208496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2510901689529419},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16465803980827332},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.14381983876228333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12638524174690247},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09841197729110718}],"concepts":[{"id":"https://openalex.org/C89451469","wikidata":"https://www.wikidata.org/wiki/Q1443036","display_name":"Parseval's theorem","level":5,"score":0.8942183256149292},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7010469436645508},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.562872588634491},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.5527082681655884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5449870228767395},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5240352749824524},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.45755043625831604},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4196814000606537},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4050019085407257},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39269453287124634},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3890443444252014},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36736738681793213},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3284938931465149},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.2872140109539032},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26893019676208496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2510901689529419},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16465803980827332},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.14381983876228333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12638524174690247},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09841197729110718},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691320500095","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691320500095","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":24,"referenced_works":["https://openalex.org/W224962721","https://openalex.org/W646009186","https://openalex.org/W1570190641","https://openalex.org/W1594563152","https://openalex.org/W1983997081","https://openalex.org/W1985459260","https://openalex.org/W2015705083","https://openalex.org/W2021488232","https://openalex.org/W2042945488","https://openalex.org/W2054710922","https://openalex.org/W2062512227","https://openalex.org/W2068577982","https://openalex.org/W2078623209","https://openalex.org/W2083446386","https://openalex.org/W2100416548","https://openalex.org/W2110157363","https://openalex.org/W2117061778","https://openalex.org/W2155400999","https://openalex.org/W2164829628","https://openalex.org/W2164964910","https://openalex.org/W2485050050","https://openalex.org/W4214523560","https://openalex.org/W4255272544","https://openalex.org/W4292170079"],"related_works":["https://openalex.org/W1994351836","https://openalex.org/W2176075524","https://openalex.org/W1484727951","https://openalex.org/W2379859495","https://openalex.org/W1553824813","https://openalex.org/W4246648935","https://openalex.org/W2032074140","https://openalex.org/W2040760337","https://openalex.org/W2111953915","https://openalex.org/W2353472794"],"abstract_inverted_index":{"Frame":[0],"multiresolution":[1],"analysis":[2],"(FMRA)":[3],"in":[4,12,27,101],"[Formula:":[5,28,61,73,98,102,110,123],"see":[6,29,62,74,99,103,111,124],"text]":[7,75,100,104,125],"is":[8,44,136],"an":[9,168,174],"important":[10],"topic":[11],"frame":[13,145],"theory":[14,172],"and":[15,35,54,68,92,122,135,167],"its":[16,159],"applications.":[17],"In":[18],"this":[19],"paper,":[20],"we":[21,149],"consider":[22],"the":[23,48,56,77,114,119,130,152,156,165,171],"so-called":[24],"multiscaling":[25,86,120],"FMRA":[26,53,121],"text],":[30],"which":[31],"has":[32],"matrix":[33],"dilations":[34],"a":[36,45,85],"finite":[37],"number":[38],"of":[39,47,59,109,132,146,155,158,170],"scaling":[40],"functions.":[41],"This":[42],"framework":[43],"generalization":[46],"theories":[49],"both":[50],"on":[51,55,118],"monoscaling":[52],"classical":[57],"MRA":[58],"multiplicity":[60],"text].":[63,112],"We":[64,88,163],"characterize":[65],"wavelet":[66,70],"frames":[67,71],"Parseval":[69],"for":[72,95,142],"under":[76],"circumstances":[78],"that":[79],"they":[80],"can":[81],"be":[82,106],"associated":[83],"with":[84,173],"FMRA.":[87],"give":[89,150],"two":[90],"necessary":[91],"sufficient":[93],"conditions":[94],"given":[96],"functions":[97],"to":[105,139],"multiframe":[107],"generators":[108,157],"Especially,":[113],"second":[115],"condition":[116],"depends":[117],"only,":[126],"does":[127],"not":[128],"require":[129],"existence":[131],"other":[133],"functions,":[134],"relatively":[137],"easier":[138],"verify.":[140],"Moreover,":[141],"any":[143],"finitely-generated":[144],"integer":[147],"translates,":[148],"explicitly":[151],"Fourier":[153],"transforms":[154],"canonical":[160],"dual":[161],"frame.":[162],"illustrate":[164],"implementation":[166],"application":[169],"example.":[175]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}