{"id":"https://openalex.org/W2126414379","doi":"https://doi.org/10.1142/s0219691314600030","title":"Continuous quaternion fourier and wavelet transforms","display_name":"Continuous quaternion fourier and wavelet transforms","publication_year":2014,"publication_date":"2014-02-07","ids":{"openalex":"https://openalex.org/W2126414379","doi":"https://doi.org/10.1142/s0219691314600030","mag":"2126414379"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691314600030","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691314600030","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/A5051144697","display_name":"Mawardi Bahri","orcid":"https://orcid.org/0000-0003-1628-9163"},"institutions":[{"id":"https://openalex.org/I98301867","display_name":"Hasanuddin University","ror":"https://ror.org/00da1gf19","country_code":"ID","type":"education","lineage":["https://openalex.org/I98301867"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Mawardi Bahri","raw_affiliation_strings":["Department of Mathematics, Universitas Hasanuddin, Makassar 90245, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universitas Hasanuddin, Makassar 90245, Indonesia","institution_ids":["https://openalex.org/I98301867"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085378838","display_name":"Ryuichi Ashino","orcid":"https://orcid.org/0000-0003-4807-4300"},"institutions":[{"id":"https://openalex.org/I141479679","display_name":"Osaka Kyoiku University","ror":"https://ror.org/051j8zv27","country_code":"JP","type":"education","lineage":["https://openalex.org/I141479679"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ryuichi Ashino","raw_affiliation_strings":["Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japan","institution_ids":["https://openalex.org/I141479679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109371455","display_name":"R\u00e9mi Vaillancourt","orcid":null},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R\u00e9mi Vaillancourt","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada K1N 6N5, Canada","institution_ids":["https://openalex.org/I153718931"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6493,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.92632413,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"12","issue":"04","first_page":"1460003","last_page":"1460003"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9990000128746033,"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":0.9990000128746033,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9976000189781189,"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":0.9876000285148621,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.7020056247711182},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6898337602615356},{"id":"https://openalex.org/keywords/quaternion-algebra","display_name":"Quaternion algebra","score":0.5539137125015259},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5306854248046875},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5236939191818237},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5089645385742188},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.47128644585609436},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4579417407512665},{"id":"https://openalex.org/keywords/convolution-theorem","display_name":"Convolution theorem","score":0.4327079951763153},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42738574743270874},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.30960869789123535},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.26457786560058594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10401245951652527},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0814085304737091},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0807458758354187},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.07531312108039856},{"id":"https://openalex.org/keywords/cellular-algebra","display_name":"Cellular algebra","score":0.06925740838050842}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.7020056247711182},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6898337602615356},{"id":"https://openalex.org/C151640129","wikidata":"https://www.wikidata.org/wiki/Q2835967","display_name":"Quaternion algebra","level":5,"score":0.5539137125015259},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5306854248046875},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5236939191818237},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5089645385742188},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.47128644585609436},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4579417407512665},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.4327079951763153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42738574743270874},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.30960869789123535},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.26457786560058594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10401245951652527},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0814085304737091},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0807458758354187},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.07531312108039856},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.06925740838050842},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219691314600030","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691314600030","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"},{"id":"pmh:oai:repository.unhas.ac.id:123456789/11395","is_oa":false,"landing_page_url":"http://repository.unhas.ac.id/handle/123456789/11395","pdf_url":null,"source":{"id":"https://openalex.org/S4406922391","display_name":"Hasanuddin University Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6070704638","display_name":"Source separation using N-tree discrete wavelet transform and sparse representation","funder_award_id":"26400199","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W607200110","https://openalex.org/W1970012920","https://openalex.org/W1972673941","https://openalex.org/W1973037749","https://openalex.org/W1998134128","https://openalex.org/W2002372305","https://openalex.org/W2028139062","https://openalex.org/W2046410074","https://openalex.org/W2049120232","https://openalex.org/W2058558325","https://openalex.org/W2062853976","https://openalex.org/W2081550440","https://openalex.org/W2082847977","https://openalex.org/W2086055091","https://openalex.org/W2115755118","https://openalex.org/W2137584359","https://openalex.org/W2145412836","https://openalex.org/W2153300685","https://openalex.org/W2155973954","https://openalex.org/W2161478868","https://openalex.org/W2230420325","https://openalex.org/W2567235724","https://openalex.org/W3021706340","https://openalex.org/W3022578592","https://openalex.org/W3099653240","https://openalex.org/W3102858728","https://openalex.org/W3175575010","https://openalex.org/W4232174397","https://openalex.org/W4298346532"],"related_works":["https://openalex.org/W2058788062","https://openalex.org/W4362700167","https://openalex.org/W775106713","https://openalex.org/W2946572075","https://openalex.org/W4291249731","https://openalex.org/W2949247699","https://openalex.org/W2377268185","https://openalex.org/W4297956193","https://openalex.org/W2293685972","https://openalex.org/W4363675452"],"abstract_inverted_index":{"A":[0],"two-dimensional":[1],"(2D)":[2],"quaternion":[3,33,56],"Fourier":[4],"transform":[5,52],"(QFT)":[6],"defined":[7],"with":[8],"the":[9,41,44,59,62],"kernel":[10,60],"[Formula:":[11],"see":[12],"text]":[13],"is":[14,35,53],"proposed.":[15],"Some":[16],"fundamental":[17],"properties,":[18],"such":[19],"as":[20,37],"convolution,":[21],"Plancherel":[22],"and":[23],"vector":[24],"differential":[25,48],"theorems,":[26],"are":[27],"established.":[28],"The":[29,50],"heat":[30],"equation":[31],"in":[32],"algebra":[34,57],"presented":[36],"an":[38],"example":[39],"of":[40,43,61],"application":[42],"QFT":[45],"to":[46,55],"partial":[47],"equations.":[49],"wavelet":[51],"extended":[54],"using":[58],"QFT.":[63]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}