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Multi-wavelets from B-spline super-functions with approximation order

Ozkaramanli, Huseyin, Bhatti, Asim and Bilgehan, Bulent 2002, Multi-wavelets from B-spline super-functions with approximation order, Signal processing, vol. 82, no. 8, pp. 1029-1046.


Title Multi-wavelets from B-spline super-functions with approximation order
Author(s) Ozkaramanli, Huseyin
Bhatti, Asim
Bilgehan, Bulent
Journal name Signal processing
Volume number 82
Issue number 8
Start page 1029
End page 1046
Publisher Elsevier BV
Place of publication Amsterdam, Netherlands
Publication date 2002-08
ISSN 0165-1684
Keyword(s) Multi-wavelets
Scalar wavelets
Orthogonality
Approximation order
Symmetry
Superfunction
B-spline
Summary Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix Hf; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.
Language eng
Field of Research 080106 Image Processing
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1.1 Refereed article in a scholarly journal
Copyright notice ©2002, Elsevier Science B.V
Persistent URL http://hdl.handle.net/10536/DRO/DU:30009474

Document type: Journal Article
Collection: School of Engineering and Information Technology
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