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We proved that an interpolatory mask whose center of symmetry is different from the origin cannot generate wavelets with vanishing moments of order n &gt; 0. For matrix dilations M with | det M| = 2, we also give an explicit method for construction of masks (non-interpolatory) m<jats:sub>0<\/jats:sub>symmetric with respect to a semi-integer point and providing vanishing moments up to arbitrary order n. It is proved that for some matrix dilations (in particular, for the quincunx matrix) such a mask does not have a dual mask. Some of the constructed masks were successfully applied for signal processes.<\/jats:p>","DOI":"10.1142\/s0219691309002921","type":"journal-article","created":{"date-parts":[[2009,5,22]],"date-time":"2009-05-22T09:12:52Z","timestamp":1242983572000},"page":"313-340","source":"Crossref","is-referenced-by-count":9,"title":["SYMMETRIC MULTIVARIATE WAVELETS"],"prefix":"10.1142","volume":"07","author":[{"given":"S.","family":"KARAKAZ'YAN","sequence":"first","affiliation":[{"name":"St. Petersburg State University for Architecture and Building, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"SKOPINA","sequence":"additional","affiliation":[{"name":"St. Petersburg State University, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"TCHOBANOU","sequence":"additional","affiliation":[{"name":"Moscow Power Engineering Institute, Technical University, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2002.1010038"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(87)90219-8"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/83.855441"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2003.809619"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02511222"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018950126225"},{"key":"rf8","first-page":"40","volume":"16","author":"Chernikov A.","journal-title":"Cifrovaya Obrabotka Signalov (Digital Signal Processing)"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970104"},{"key":"rf10","first-page":"207","volume":"35","author":"Han B.","journal-title":"Linear Algebra Appl."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-98-00925-9"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500006076"},{"key":"rf13","first-page":"1221","volume":"3","author":"Kingsbury N.","journal-title":"IEEE Trans. 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