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Compactly Supported Orthogonal and Biorthogonal \sqrt 5 -Refinement Wavelets With 4-Fold Symmetry

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1 Author(s)
Qingtang Jiang ; Dept. of Math. & Comput. Sci., Univ. of Missouri-St. Louis, St. Louis, MO

Recently, radic5 -refinement hierarchical sampling has been studied and radic5-refinement has been used for surface subdivision. Compared with other refinements, such as the dyadic or quincunx refinement, radic5-refinement has a special property that the nodes in a refined lattice form groups of five nodes with these five nodes having different x and y coordinates. This special property has been shown to be very useful to represent adaptively and render complex and procedural geometry. When radic5-refinement is used for multiresolution data processing, radic5-refinement filter banks and wavelets are required. While the construction of 2-D nonseparable (bi)orthogonal wavelets with the dyadic or quincunx refinement has been studied by many researchers, the construction of (bi)orthogonal wavelets with radic5-refinement has not been investigated. The main goal of this paper is to construct compactly supported orthogonal and biorthogonal wavelets with radic5 -refinement. In this paper, we obtain block structures of orthogonal and biorthogonal radic5-refinement FIR filter banks with 4-fold rotational symmetry. We construct compactly supported orthogonal and biorthogonal wavelets based on these block structures.

Published in:

Image Processing, IEEE Transactions on  (Volume:17 ,  Issue: 11 )

Date of Publication:

Nov. 2008

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