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, doi: 10.1016/S0165-1684(02)00212-8.

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Title Multi-wavelets from B-spline super-functions with approximation order
Author(s) Ozkaramanli, Huseyin
Bhatti, AsimORCID iD for 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
Approximation order
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
DOI 10.1016/S0165-1684(02)00212-8
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
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Document type: Journal Article
Collection: School of Engineering and Information Technology
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