{"id":"https://openalex.org/W2963310456","doi":"https://doi.org/10.1109/tit.2016.2608896","title":"Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks With Fast Algorithms","display_name":"Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks With Fast Algorithms","publication_year":2016,"publication_date":"2016-09-13","ids":{"openalex":"https://openalex.org/W2963310456","doi":"https://doi.org/10.1109/tit.2016.2608896","mag":"2963310456"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2608896","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2608896","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5024513674","display_name":"Youngmi Hur","orcid":"https://orcid.org/0000-0001-9547-9533"},"institutions":[{"id":"https://openalex.org/I193775966","display_name":"Yonsei University","ror":"https://ror.org/01wjejq96","country_code":"KR","type":"education","lineage":["https://openalex.org/I193775966"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Youngmi Hur","raw_affiliation_strings":["Department of Mathematics, Yonsei University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0001-9547-9533","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Yonsei University, Seoul, South Korea","institution_ids":["https://openalex.org/I193775966"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041679034","display_name":"Fang Zheng","orcid":"https://orcid.org/0000-0002-7858-4080"},"institutions":[{"id":"https://openalex.org/I4210112894","display_name":"Ernst & Young (United States)","ror":"https://ror.org/02c00bp33","country_code":"US","type":"company","lineage":["https://openalex.org/I4210108721","https://openalex.org/I4210112894"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fang Zheng","raw_affiliation_strings":["Financial Services Risk Management, Ernst & Young, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Financial Services Risk Management, Ernst & Young, New York, NY, USA","institution_ids":["https://openalex.org/I4210112894"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.338,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70472946,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"62","issue":"11","first_page":"6580","last_page":"6593"},"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9973999857902527,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/wavelet","display_name":"Wavelet","score":0.7684745192527771},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6482475996017456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5700700283050537},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.5561964511871338},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5388088226318359},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.4611750841140747},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.46103763580322266},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43960192799568176},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.43598946928977966},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.4124871790409088},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37290164828300476},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2999165654182434},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18874433636665344},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1616901159286499},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1529744267463684},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.10072663426399231}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7684745192527771},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6482475996017456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5700700283050537},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.5561964511871338},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5388088226318359},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.4611750841140747},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.46103763580322266},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43960192799568176},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.43598946928977966},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.4124871790409088},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37290164828300476},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2999165654182434},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18874433636665344},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1616901159286499},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1529744267463684},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.10072663426399231}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2016.2608896","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2608896","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5939273869","display_name":null,"funder_award_id":"DMS-1115870","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G632440860","display_name":null,"funder_award_id":"20151003262","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G8138102369","display_name":null,"funder_award_id":"20151009350","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1170769","https://openalex.org/W163345641","https://openalex.org/W614658540","https://openalex.org/W1481646516","https://openalex.org/W1485280399","https://openalex.org/W1598325079","https://openalex.org/W1658679052","https://openalex.org/W1952194262","https://openalex.org/W1963500053","https://openalex.org/W1963738274","https://openalex.org/W1981505368","https://openalex.org/W1986195633","https://openalex.org/W1989619792","https://openalex.org/W2000489837","https://openalex.org/W2017678253","https://openalex.org/W2027294860","https://openalex.org/W2028736438","https://openalex.org/W2031299600","https://openalex.org/W2045952578","https://openalex.org/W2048582401","https://openalex.org/W2051656206","https://openalex.org/W2053954066","https://openalex.org/W2067393519","https://openalex.org/W2072307436","https://openalex.org/W2072357243","https://openalex.org/W2080333741","https://openalex.org/W2087235358","https://openalex.org/W2090374302","https://openalex.org/W2098288204","https://openalex.org/W2101993234","https://openalex.org/W2111901314","https://openalex.org/W2117853853","https://openalex.org/W2127547766","https://openalex.org/W2132534805","https://openalex.org/W2132680427","https://openalex.org/W2132984323","https://openalex.org/W2134397503","https://openalex.org/W2143316745","https://openalex.org/W2146846625","https://openalex.org/W2155962605","https://openalex.org/W2156877470","https://openalex.org/W2157096733","https://openalex.org/W2166796177","https://openalex.org/W2168913557","https://openalex.org/W2294576049","https://openalex.org/W2893968183","https://openalex.org/W6600055216","https://openalex.org/W6679991515","https://openalex.org/W7058708535"],"related_works":["https://openalex.org/W2144834862","https://openalex.org/W1985382169","https://openalex.org/W160861300","https://openalex.org/W2364473262","https://openalex.org/W2149628758","https://openalex.org/W2017976005","https://openalex.org/W3125711196","https://openalex.org/W2098466859","https://openalex.org/W2142684386","https://openalex.org/W2364469601"],"abstract_inverted_index":{"As":[0],"constructing":[1],"multi-D":[2,19,29,72,92],"wavelets":[3],"remains":[4],"a":[5,10,24],"challenging":[6],"problem,":[7],"we":[8],"propose":[9],"new":[11],"method":[12,22,46],"called":[13],"prime":[14,63],"coset":[15],"sum":[16],"to":[17,27],"construct":[18,28],"wavelets.":[20],"Our":[21,45],"provides":[23],"systematic":[25],"way":[26],"non-separable":[30],"wavelet":[31,73,93],"filter":[32,74,94],"banks":[33,75,95],"from":[34],"two":[35],"1-D":[36,84],"low-pass":[37,85],"filters,":[38,86],"with":[39,98],"one":[40],"of":[41,70,81],"which":[42],"being":[43],"interpolatory.":[44],"has":[47],"many":[48],"important":[49],"features":[50],"including":[51],"the":[52,67,71,82,90,105],"following:":[53],"1)":[54],"it":[55],"works":[56],"for":[57],"any":[58,62],"spatial":[59],"dimension,":[60],"and":[61,87],"scalar":[64],"dilation;":[65],"2)":[66],"vanishing":[68],"moments":[69],"are":[76,96,102],"guaranteed":[77],"by":[78],"certain":[79],"properties":[80],"initial":[83],"furthermore;":[88],"3)":[89],"resulting":[91],"associated":[97],"fast":[99,107],"algorithms":[100],"that":[101],"faster":[103],"than":[104],"existing":[106],"tensor":[108],"product":[109],"algorithms.":[110]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}