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

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.