{"id":"https://openalex.org/W2088583515","doi":"https://doi.org/10.1137/s1064827596311906","title":"Multiresolution Analysis and Supercompact Multiwavelets","display_name":"Multiresolution Analysis and Supercompact Multiwavelets","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2088583515","doi":"https://doi.org/10.1137/s1064827596311906","mag":"2088583515"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827596311906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596311906","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5017494370","display_name":"Richard M. Beam","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Richard M. Beam","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083147050","display_name":"R. F. Warming","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert F. Warming","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017494370"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9748,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.87815739,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"4","first_page":"1238","last_page":"1268"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9898999929428101,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9700999855995178,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.8372728228569031},{"id":"https://openalex.org/keywords/multiresolution-analysis","display_name":"Multiresolution analysis","score":0.7912953495979309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7523366212844849},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7237739562988281},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.5752997994422913},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5679637789726257},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.5432206392288208},{"id":"https://openalex.org/keywords/haar","display_name":"Haar","score":0.5008945465087891},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5005159378051758},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4868995249271393},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4541061818599701},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.44599324464797974},{"id":"https://openalex.org/keywords/constant-function","display_name":"Constant function","score":0.44513943791389465},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4378580152988434},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.43544289469718933},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.42191511392593384},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.42055708169937134},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4122934937477112},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34240877628326416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3262448310852051},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.3053353428840637},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16388115286827087},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.1497272253036499},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14227458834648132},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07574459910392761}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8372728228569031},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.7912953495979309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7523366212844849},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7237739562988281},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.5752997994422913},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5679637789726257},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5432206392288208},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.5008945465087891},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5005159378051758},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4868995249271393},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4541061818599701},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.44599324464797974},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.44513943791389465},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4378580152988434},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.43544289469718933},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.42191511392593384},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.42055708169937134},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4122934937477112},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34240877628326416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3262448310852051},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.3053353428840637},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16388115286827087},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.1497272253036499},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14227458834648132},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07574459910392761},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827596311906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596311906","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":8,"referenced_works":["https://openalex.org/W823103609","https://openalex.org/W1568710730","https://openalex.org/W1996164095","https://openalex.org/W2041752335","https://openalex.org/W2048247182","https://openalex.org/W2065914862","https://openalex.org/W2098914003","https://openalex.org/W2100917607"],"related_works":["https://openalex.org/W2766849256","https://openalex.org/W4361795924","https://openalex.org/W984746159","https://openalex.org/W1523827626","https://openalex.org/W1999916501","https://openalex.org/W4232769230","https://openalex.org/W2005569824","https://openalex.org/W1883376054","https://openalex.org/W1661063387","https://openalex.org/W2120097785"],"abstract_inverted_index":{"The":[0,10,78],"Haar":[1,90],"wavelets":[2],"can":[3,24],"represent":[4,25],"exactly":[5,26],"any":[6,27],"piecewise":[7,28,101],"constant":[8],"function.":[9,30],"motivation":[11],"for":[12],"the":[13,35,38,51,59,65,69,72,76,85,89,95],"present":[14],"development":[15],"is":[16,68],"Alpert's":[17],"family":[18],"of":[19,42,58,71,88],"compact":[20],"orthogonal":[21],"multiwavelets":[22,49],"that":[23],"polynomial":[29],"We":[31,53],"choose":[32],"to":[33,48,98],"derive":[34],"algorithm":[36,96],"in":[37],"style":[39],"and":[40,74,100],"notation":[41],"Harten's":[43],"multiresolution":[44],"analysis":[45],"as":[46],"extended":[47],"by":[50],"authors.":[52],"begin":[54],"with":[55],"a":[56],"description":[57],"nested":[60],"grid":[61],"hierarchy.":[62],"Next":[63],"comes":[64],"decomposition,":[66],"which":[67,93],"heart":[70],"algorithm,":[73],"finally":[75],"reconstruction.":[77],"basis":[79,91],"functions":[80],"(which":[81],"are":[82],"nonfractal)":[83],"retain":[84],"spatial":[86],"compactness":[87],"functions,":[92],"enhances":[94],"application":[97],"nonperiodic":[99],"continuous":[102],"data.":[103]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}