{"id":"https://openalex.org/W2015391631","doi":"https://doi.org/10.1090/s0025-5718-04-01681-3","title":"Balanced multi-wavelets in \u211d^{\ud835\udd64}","display_name":"Balanced multi-wavelets in \u211d^{\ud835\udd64}","publication_year":2004,"publication_date":"2004-06-07","ids":{"openalex":"https://openalex.org/W2015391631","doi":"https://doi.org/10.1090/s0025-5718-04-01681-3","mag":"2015391631"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-04-01681-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01681-3","pdf_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-04-01681-3/S0025-5718-04-01681-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-04-01681-3/S0025-5718-04-01681-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103210224","display_name":"Charles K. Chui","orcid":"https://orcid.org/0000-0003-2482-8980"},"institutions":[{"id":"https://openalex.org/I208333798","display_name":"University of Missouri\u2013St. Louis","ror":"https://ror.org/037cnag11","country_code":"US","type":"education","lineage":["https://openalex.org/I208333798"]},{"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":true,"raw_author_name":"Charles Chui","raw_affiliation_strings":["Department of Mathematics & Computer Science, University of Missouri\u00e2\u0080\u0093St. Louis, St. Louis, Missouri 63121 and Department of Statistics, Stanford University, Stanford, California 94305","Department of Mathematics and Computer Science, University of Missouri\u2013St. Louis, St. Louis, Missouri 63121 and Department of Statistics, Stanford University, Stanford, California 94305"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Computer Science, University of Missouri\u00e2\u0080\u0093St. Louis, St. Louis, Missouri 63121 and Department of Statistics, Stanford University, Stanford, California 94305","institution_ids":["https://openalex.org/I208333798","https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Missouri\u2013St. Louis, St. Louis, Missouri 63121 and Department of Statistics, Stanford University, Stanford, California 94305","institution_ids":["https://openalex.org/I208333798"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027322245","display_name":"Qingtang Jiang","orcid":"https://orcid.org/0000-0002-0173-9988"},"institutions":[{"id":"https://openalex.org/I208333798","display_name":"University of Missouri\u2013St. Louis","ror":"https://ror.org/037cnag11","country_code":"US","type":"education","lineage":["https://openalex.org/I208333798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qingtang Jiang","raw_affiliation_strings":["Department of Mathematics & Computer Science, University of Missouri\u00e2\u0080\u0093St. Louis, St. Louis, Missouri 63121","Department of Mathematics and Computer Science, University of Missouri\u2014St. Louis, St. Louis, Missouri 63121"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Computer Science, University of Missouri\u00e2\u0080\u0093St. Louis, St. Louis, Missouri 63121","institution_ids":["https://openalex.org/I208333798"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Missouri\u2014St. Louis, St. Louis, Missouri 63121","institution_ids":["https://openalex.org/I208333798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103210224"],"corresponding_institution_ids":["https://openalex.org/I208333798","https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":1.6562,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.84599411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"74","issue":"251","first_page":"1323","last_page":"1344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998999834060669,"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":0.9998999834060669,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9952999949455261,"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":0.7964701652526855},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6269460320472717},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5541710257530212},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.5512083172798157},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5142537951469421},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5091449618339539},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.48842066526412964},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.46863269805908203},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41804760694503784},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.41725805401802063},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.380166620016098},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3509013056755066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27763134241104126},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1275639832019806},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0975024402141571},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0896308422088623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7964701652526855},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6269460320472717},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5541710257530212},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.5512083172798157},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5142537951469421},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5091449618339539},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.48842066526412964},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.46863269805908203},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41804760694503784},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.41725805401802063},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.380166620016098},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3509013056755066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27763134241104126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1275639832019806},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0975024402141571},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0896308422088623},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-04-01681-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01681-3","pdf_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-04-01681-3/S0025-5718-04-01681-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-04-01681-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01681-3","pdf_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-04-01681-3/S0025-5718-04-01681-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G533150958","display_name":"Spline-Wavelet Frames in Computer Graphics and other Applications","funder_award_id":"0098331","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5752015503","display_name":"Tight Frames of Rational Splines and Application to CAD/CAM and Computer Graphics","funder_award_id":"9988289","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309568","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06"},{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2015391631.pdf","grobid_xml":"https://content.openalex.org/works/W2015391631.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W192322834","https://openalex.org/W1277493121","https://openalex.org/W1492181480","https://openalex.org/W1510656098","https://openalex.org/W1966975678","https://openalex.org/W2048247182","https://openalex.org/W2099688137","https://openalex.org/W2109411320","https://openalex.org/W2116124511","https://openalex.org/W2120741170","https://openalex.org/W2125620133","https://openalex.org/W2126323701","https://openalex.org/W2141858002","https://openalex.org/W2143294992","https://openalex.org/W2143601630","https://openalex.org/W2158821445","https://openalex.org/W2164364763","https://openalex.org/W2169035906","https://openalex.org/W4303117174"],"related_works":["https://openalex.org/W2370850565","https://openalex.org/W2381894435","https://openalex.org/W2296214397","https://openalex.org/W2951195293","https://openalex.org/W2029951831","https://openalex.org/W1975945902","https://openalex.org/W2392110000","https://openalex.org/W2168986779","https://openalex.org/W953696202","https://openalex.org/W2109783141"],"abstract_inverted_index":{"The":[0,218],"notion":[1],"of":[2,29,40,42,47,103,135,220,228,260],"<inline-formula":[3,49,64,110,137,153,188,230,279],"content-type=\"math/mathml\">":[4,50,65,111,138,154,189,231,280],"<mml:math":[5,51,66,112,139,155,190,232,281],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,52,67,113,140,156,191,233,282],"alttext=\"upper":[7,53,68,114,141,157,192,234,283],"K\">":[8,54,142,235],"<mml:semantics>":[9,55,72,118,143,161,196,236,287],"<mml:mi>K</mml:mi>":[10,56,74,120,144,163,198,237,289],"<mml:annotation":[11,57,80,124,145,169,202,238,295],"encoding=\"application/x-tex\">K</mml:annotation>":[12,58,146,239],"</mml:semantics>":[13,59,82,126,147,172,204,240,298],"</mml:math>":[14,60,83,127,148,173,205,241,299],"</inline-formula>":[15,61,84,128,149,174,206,242,300],"-balancing":[16,150,243],"was":[17],"introduced":[18],"a":[19,24,183],"few":[20,185],"years":[21],"ago":[22],"as":[23,251,253],"condition":[25,96,151,244],"for":[26,109,152,187,262,277],"the":[27,38,89,101,107,133,136,215,229,247,258,263,271],"construction":[28,264],"orthonormal":[30],"scaling":[31],"function":[32],"vectors":[33],"and":[34,207,274],"multi-wavelets":[35],"to":[36,100,179,224],"ensure":[37],"property":[39,250],"preservation/annihilation":[41],"scalar-valued":[43],"discrete":[44],"polynomial":[45,248],"data":[46],"order":[48],"(or":[62],"degree":[63],"K":[69,115,158,193,284],"minus":[70],"1\">":[71,117,286],"<mml:mrow>":[73,119,162,197,288],"<mml:mo>":[75,164,290],"\u2212":[76],"</mml:mo>":[77,166,292],"<mml:mn>1</mml:mn>":[78,122,293],"</mml:mrow>":[79,123,168,201,294],"encoding=\"application/x-tex\">K-1</mml:annotation>":[81],"),":[85],"when":[86],"decomposed":[87],"by":[88],"corresponding":[90],"matrix-valued":[91],"low-pass/high-pass":[92],"filters.":[93],"While":[94],"this":[95,221],"is":[97,129,175,223],"indeed":[98],"precise,":[99],"best":[102],"our":[104],"knowledge":[105],"only":[106,182],"proof":[108],"equals":[116,194],"<mml:mo>=</mml:mo>":[121,199],"encoding=\"application/x-tex\">K=1</mml:annotation>":[125],"known.":[130],"In":[131],"addition,":[132],"formulation":[134],"greater-than-or-equal-to":[159,285],"2\">":[160,195],"\u2265":[165,291],"<mml:mn>2</mml:mn>":[167,200],"encoding=\"application/x-tex\">K\\ge":[170,296],"2</mml:annotation>":[171],"so":[176],"prohibitively":[177],"difficult":[178],"satisfy":[180],"that":[181,245,256],"very":[184],"examples":[186],"encoding=\"application/x-tex\">K=2</mml:annotation>":[203],"vector":[208],"dimension":[209],"2":[210],"have":[211],"been":[212],"constructed":[213],"in":[214,270],"open":[216],"literature.":[217],"objective":[219],"paper":[222],"derive":[225],"various":[226],"characterizations":[227],"include":[246],"preservation":[249],"well":[252],"equivalent":[254],"formulations":[255],"facilitate":[257],"development":[259],"methods":[261],"purpose.":[265],"These":[266],"results":[267],"are":[268],"established":[269],"general":[272],"multivariate":[273],"bi-orthogonal":[275],"settings":[276],"any":[278],"1</mml:annotation>":[297],".":[301]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":7},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}