{"id":"https://openalex.org/W2133528803","doi":"https://doi.org/10.1109/tsp.2008.2007097","title":"Overcomplete Discrete Wavelet Transforms With Rational Dilation Factors","display_name":"Overcomplete Discrete Wavelet Transforms With Rational Dilation Factors","publication_year":2008,"publication_date":"2008-11-06","ids":{"openalex":"https://openalex.org/W2133528803","doi":"https://doi.org/10.1109/tsp.2008.2007097","mag":"2133528803"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2008.2007097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2008.2007097","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal 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/A5046157113","display_name":"\u0130lker Bayram","orcid":"https://orcid.org/0000-0002-4829-5827"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ilker Bayram","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA","Dept. of Electr. & Comput. Eng., Polytech. Inst. of New York Univ., Brooklyn, OH"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA","institution_ids":["https://openalex.org/I90965887","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Polytech. Inst. of New York Univ., Brooklyn, OH","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058321875","display_name":"Ivan Selesnick","orcid":"https://orcid.org/0000-0002-4939-3971"},"institutions":[{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ivan W. Selesnick","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA","Dept. of Electr. & Comput. Eng., Polytech. Inst. of New York Univ., Brooklyn, OH"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, USA","institution_ids":["https://openalex.org/I90965887","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Polytech. Inst. of New York Univ., Brooklyn, OH","institution_ids":["https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046157113"],"corresponding_institution_ids":["https://openalex.org/I57206974","https://openalex.org/I90965887"],"apc_list":null,"apc_paid":null,"fwci":4.9694,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.9557395,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"57","issue":"1","first_page":"131","last_page":"145"},"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":0.9951000213623047,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9866999983787537,"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/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.6521263122558594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6405923366546631},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.5898594260215759},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5794470906257629},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5481860041618347},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4231453537940979},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.41641002893447876},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.313467413187027},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2928559482097626},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2740653455257416},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22440865635871887}],"concepts":[{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.6521263122558594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6405923366546631},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5898594260215759},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5794470906257629},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5481860041618347},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4231453537940979},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.41641002893447876},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.313467413187027},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2928559482097626},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2740653455257416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22440865635871887},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2008.2007097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2008.2007097","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.2974","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.2974","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://taco.poly.edu/selesi/rational/Rational_Dilation_2009_TSP_preprint.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.3846","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.3846","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://taco.poly.edu/selesi/rational/Rational_Dilation_2009_TSP.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W17264277","https://openalex.org/W94169221","https://openalex.org/W154292103","https://openalex.org/W186879748","https://openalex.org/W619413120","https://openalex.org/W1481646516","https://openalex.org/W1545748428","https://openalex.org/W1557809948","https://openalex.org/W1562327279","https://openalex.org/W1595505223","https://openalex.org/W1610060839","https://openalex.org/W1802935330","https://openalex.org/W1900372236","https://openalex.org/W1964850409","https://openalex.org/W1984699259","https://openalex.org/W1985738912","https://openalex.org/W1987172946","https://openalex.org/W1993077418","https://openalex.org/W2003370853","https://openalex.org/W2022394579","https://openalex.org/W2023723226","https://openalex.org/W2043583598","https://openalex.org/W2044578857","https://openalex.org/W2062024414","https://openalex.org/W2065675029","https://openalex.org/W2067204686","https://openalex.org/W2071039517","https://openalex.org/W2072595795","https://openalex.org/W2082415706","https://openalex.org/W2096708025","https://openalex.org/W2096971955","https://openalex.org/W2101789093","https://openalex.org/W2103504761","https://openalex.org/W2106515586","https://openalex.org/W2107790757","https://openalex.org/W2113643684","https://openalex.org/W2129276048","https://openalex.org/W2133886987","https://openalex.org/W2137440839","https://openalex.org/W2140940213","https://openalex.org/W2143257348","https://openalex.org/W2144682333","https://openalex.org/W2156757852","https://openalex.org/W2163101083","https://openalex.org/W2165783715","https://openalex.org/W4232686722","https://openalex.org/W4233705760","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W2085792030","https://openalex.org/W1588899229","https://openalex.org/W2023142747","https://openalex.org/W2172291505","https://openalex.org/W2063036707","https://openalex.org/W2037009764","https://openalex.org/W2501033992","https://openalex.org/W2377605153","https://openalex.org/W2088723847","https://openalex.org/W2039128285"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"This":[3],"paper":[4],"develops":[5],"an":[6],"overcomplete":[7,22],"discrete":[8],"wavelet":[9],"transform":[10],"(DWT)":[11],"based":[12,79],"on":[13,80],"rational":[14,23,69],"dilation":[15],"factors":[16],"for":[17,50],"discrete-time":[18],"signals.":[19],"The":[20,76,84],"proposed":[21],"DWT":[24],"is":[25,32,48,74,78],"implemented":[26],"using":[27],"self-inverting":[28],"FIR":[29],"filter":[30],"banks,":[31],"approximately":[33],"shift-invariant,":[34],"and":[35,93],"can":[36,89,94],"provide":[37],"a":[38,59],"dense":[39],"sampling":[40],"of":[41,53,62,102],"the":[42,51,67,100,103],"time-frequency":[43],"plane.":[44],"A":[45],"straightforward":[46],"algorithm":[47,73,77],"described":[49],"construction":[52],"minimal-length":[54],"perfect":[55],"reconstruction":[56],"filters":[57],"with":[58],"specified":[60],"number":[61],"vanishing":[63],"moments;":[64],"whereas,":[65],"in":[66],"nonredundant":[68],"case,":[70],"no":[71],"such":[72],"available.":[75],"matrix":[81],"spectral":[82],"factorization.":[83],"analysis/synthesis":[85],"functions":[86],"(discrete-time":[87],"wavelets)":[88],"be":[90,95],"very":[91],"smooth":[92],"designed":[96],"to":[97],"closely":[98],"approximate":[99],"derivatives":[101],"Gaussian":[104],"function.":[105],"</para>":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-18T08:16:58.900851","created_date":"2025-10-10T00:00:00"}