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Subsampling Matrices for Wavelet Decompositions on Body Centered Cubic Lattices

Abstract

This article derives a family of dilation matrices for the body-centered cubic (BCC) lattice, which is optimal in the sense of spectral sphere packing. While satisfying the necessary conditions for dilation, these matrices are all cube roots of an integer scalar matrix. This property offers theoretical advantages for construction of wavelet functions in addition to the practical advantages when iterating through a perfect reconstruction filter bank based on BCC downsampling. Lastly, we factor the BCC matrix into two matrices that allow us to cascade two twochannel perfect reconstruction filter banks in order to construct a four-channel perfect reconstruction filter bank based on BCC downsampling.

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Supplemental Material
Citation
Category
Journal Paper
Divisions
Visualization and Data Analysis
Subjects
Computergraphik
Journal or Publication Title
IEEE Signal Processing Letters
ISSN
1070-9908
Date
September 2004
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