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Proceedings Paper

Extension of the concept of wavelet to vector functions
Author(s): Spartak Rafayelyan; Edward Danielian; Jaakko T. Astola; Karen O. Egiazarian
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Paper Abstract

Let Ln2 equals L2 (R) X L2 (R) X ... X L2 (R)/n. It is shown how to construct a system of functions {(phi) k (x)} equals {(phi) k(1) (x), (phi) k(2) (x), ..., (phi) k(n) (x)} from Ln2 which satisfies the following conditions: (1) After normalization it forms a Riesz basis in Ln2; (2) For any given set of functions [f1(x), f2(x), ..., fn(x)] (summation) Ln2 the representations fj(x) equals (Sigma) /k ck (DOT) (phi) k(j) (x), x (summation) R, j equals 1,n, hold, where the coefficients ck are defined from {(phi) k (x)} and [f1(x), f2(x),..., fn(x)].

Paper Details

Date Published: 22 May 2002
PDF: 7 pages
Proc. SPIE 4667, Image Processing: Algorithms and Systems, (22 May 2002);
Show Author Affiliations
Spartak Rafayelyan, Yerevan State Univ. (United States)
Edward Danielian, Yerevan State Univ. (United States)
Jaakko T. Astola, Tampere Univ. of Technology (Finland)
Karen O. Egiazarian, Tampere Univ. of Technology (Finland)

Published in SPIE Proceedings Vol. 4667:
Image Processing: Algorithms and Systems
Edward R. Dougherty; Jaakko T. Astola; Karen O. Egiazarian, Editor(s)

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