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Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function.<\/jats:p>","DOI":"10.1155\/2012\/846852","type":"journal-article","created":{"date-parts":[[2011,12,15]],"date-time":"2011-12-15T21:01:58Z","timestamp":1323982918000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Orthogonal Multiwavelet Frames in <i>L<\/i><sup>2<\/sup>(<i>R<\/i><sup><i>d<\/i><\/sup>)"],"prefix":"10.1155","volume":"2012","author":[{"given":"Liu","family":"Zhanwei","sequence":"first","affiliation":[]},{"given":"Hu","family":"Guoen","sequence":"additional","affiliation":[]},{"given":"Wu","family":"Guochang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,12,15]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/18.57199"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0097-0"},{"volume-title":"An Introduction to Wavelets","year":"1998","author":"Hern\u00e1ndez E.","key":"e_1_2_6_4_2"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/78.482009"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021360312348"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/83.753742"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1952-0047179-6"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-97-08913-4"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1997.0237"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2004.05.003"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.10.042"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2008.04.005"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2008.08.001"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.07.075"},{"key":"e_1_2_6_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2004.01.003"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2007.01.005"},{"key":"e_1_2_6_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2007.01.002"},{"key":"e_1_2_6_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2004.12.006"},{"key":"e_1_2_6_20_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1995.1363"},{"key":"e_1_2_6_21_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1994-1204376-4"},{"key":"e_1_2_6_22_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1995-056-1"},{"key":"e_1_2_6_23_2","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.2000.3635"},{"key":"e_1_2_6_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02648888"},{"key":"e_1_2_6_25_2","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.3079"},{"key":"e_1_2_6_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2008.12.006"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/846852.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/846852.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/846852","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:57:02Z","timestamp":1718089022000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/846852"}},"subtitle":[],"editor":[{"given":"Yuesheng","family":"Xu","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2011,12,15]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/846852"],"URL":"https:\/\/doi.org\/10.1155\/2012\/846852","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2011,12,15]]},"assertion":[{"value":"2011-06-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-10-25","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-12-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"846852"}}