{"id":"https://openalex.org/W2033639757","doi":"https://doi.org/10.1142/s0219691310003328","title":"WAVELETS WITH VANISHING MOMENTS ON THE HEISENBERG GROUP","display_name":"WAVELETS WITH VANISHING MOMENTS ON THE HEISENBERG GROUP","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2033639757","doi":"https://doi.org/10.1142/s0219691310003328","mag":"2033639757"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691310003328","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691310003328","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/A5028339110","display_name":"Yu Liu","orcid":"https://orcid.org/0000-0002-9943-4911"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YU LIU","raw_affiliation_strings":["Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, P. R. China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069295693","display_name":"Lizhong Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LIZHONG PENG","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9521,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.76597874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"08","issue":"01","first_page":"1","last_page":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9977999925613403,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/heisenberg-group","display_name":"Heisenberg group","score":0.7778440117835999},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7269839644432068},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.6332467794418335},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5727092027664185},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5380181074142456},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.4462081491947174},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.42861127853393555},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4175451397895813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3366689682006836},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2707405984401703},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.23911017179489136},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18898174166679382},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13878929615020752},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09203389286994934}],"concepts":[{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.7778440117835999},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7269839644432068},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6332467794418335},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5727092027664185},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5380181074142456},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.4462081491947174},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.42861127853393555},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4175451397895813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3366689682006836},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2707405984401703},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.23911017179489136},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18898174166679382},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13878929615020752},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09203389286994934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691310003328","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691310003328","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":[{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W48204474","https://openalex.org/W656294050","https://openalex.org/W1952194262","https://openalex.org/W1971998705","https://openalex.org/W2034623099","https://openalex.org/W2042455747","https://openalex.org/W2044564242","https://openalex.org/W2053084186","https://openalex.org/W2081687166","https://openalex.org/W2085453114","https://openalex.org/W2170314752","https://openalex.org/W2607742478"],"related_works":["https://openalex.org/W2009525028","https://openalex.org/W4321064619","https://openalex.org/W1981036054","https://openalex.org/W187158282","https://openalex.org/W183670115","https://openalex.org/W1501179639","https://openalex.org/W3199035354","https://openalex.org/W1807354010","https://openalex.org/W3143644526","https://openalex.org/W2734230146"],"abstract_inverted_index":{"Discrete":[0],"vanishing":[1,29,53],"moments":[2,30,54],"and":[3,12,55],"sum":[4,56],"rules":[5],"are":[6,45],"established":[7],"on":[8,41],"the":[9,13,23,33,42,49],"Heisenberg":[10,43],"group":[11,44],"relationship":[14],"between":[15],"them":[16],"is":[17],"investigated":[18],"in":[19],"this":[20],"paper.":[21],"Also,":[22],"compactly":[24],"supported":[25],"wavelets":[26],"with":[27],"2":[28],"corresponding":[31],"to":[32],"separable":[34],"filter":[35],"{a":[36],"m,n":[37],"h":[38],"l":[39],"}":[40],"constructed":[46],"by":[47],"using":[48],"theory":[50],"of":[51],"discrete":[52],"rules.":[57]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
