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J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p> Tight wavelet frames (TWFs) are computationally and theoretically attractive, but most existing multivariate constructions have various drawbacks, including low vanishing moments for the wavelets, or a large number of wavelet masks. We further develop existing work combining sums of squares representations with TWF construction, and present a new and general method for constructing such frames. Focusing on the case of box splines, we also demonstrate how the flexibility of our approach can lead to TWFs with high numbers of vanishing moments for all of the wavelet masks, while still having few highpass masks: in fact, we match the best known upper bound on the number of highpass masks for general box spline TWF constructions, while typically achieving much better vanishing moments for all of the wavelet masks, proving a nontrivial lower bound on this quantity. <\/jats:p>","DOI":"10.1142\/s0219691322500096","type":"journal-article","created":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T14:12:27Z","timestamp":1650291147000},"source":"Crossref","is-referenced-by-count":3,"title":["Multivariate tight wavelet frames with few generators and high vanishing moments"],"prefix":"10.1142","volume":"20","author":[{"given":"Youngmi","family":"Hur","sequence":"first","affiliation":[{"name":"Department of Mathematics, Yonsei University, Seoul 03722, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9543-9910","authenticated-orcid":false,"given":"Zachary","family":"Lubberts","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Johns Hopkins University, 3100 Wyman Park Dr, Baltimore, MD 21211, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kasso A.","family":"Okoudjou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tufts University, Medford, MA 02131, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,4,18]]},"reference":[{"key":"S0219691322500096BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02952513"},{"key":"S0219691322500096BIB002","doi-asserted-by":"publisher","DOI":"10.4171\/NEWS\/105\/4"},{"key":"S0219691322500096BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-013-9191-5"},{"key":"S0219691322500096BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2014.09.003"},{"key":"S0219691322500096BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2010.03.005"},{"key":"S0219691322500096BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S1063-5203(02)00510-9"},{"key":"S0219691322500096BIB007","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021318804341"},{"key":"S0219691322500096BIB008","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"S0219691322500096BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/S1063-5203(02)00511-0"},{"key":"S0219691322500096BIB010","series-title":"IAS Lecture Notes Series, Summer Program on The Mathematics of Image Processing","volume-title":"MRA-based Wavelet Frames and Applications","volume":"19","author":"Dong B.","year":"2010"},{"key":"S0219691322500096BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s00020-002-1198-4"},{"key":"S0219691322500096BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/2987"},{"key":"S0219691322500096BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2005.09.010"},{"key":"S0219691322500096BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(02)00891-9"},{"key":"S0219691322500096BIB015","doi-asserted-by":"publisher","DOI":"10.1137\/140988231"},{"key":"S0219691322500096BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.001"},{"key":"S0219691322500096BIB017","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2004.1428957"},{"key":"S0219691322500096BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/BF01425382"},{"key":"S0219691322500096BIB019","first-page":"532","volume":"7","author":"Rudin W.","year":"1963","journal-title":"Ill. 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Comput."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691322500096","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T08:19:35Z","timestamp":1661329175000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691322500096"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,18]]},"references-count":23,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["10.1142\/S0219691322500096"],"URL":"https:\/\/doi.org\/10.1142\/s0219691322500096","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2022,4,18]]},"article-number":"2250009"}}