Presented at the
1997 IEEE International Conference on Image Processing
Biorthogonal Quincunx Coifman Wavelets
Brian L. Evans,
Alan C. Bovik
Department of Electrical and Computer Engineering,
Engineering Science Building,
The University of Texas at Austin,
Austin, TX 78712-1084 USA
We define and construct a new family of compactly supported, nonseparable
two-dimensional wavelets, ``biorthogonal quincunx Coifman wavelets'' (BQCWs),
from their one-dimensional counterparts using the McClellan transformation.
The resulting filter banks possess many interesting properties such as
perfect reconstruction, vanishing moments, symmetry, diamond-shaped passbands,
and dyadic fractional filter coefficients.
We derive explicit formulas for the frequency responses of these filter
Both the analysis and synthesis lowpass filters converge to an ideal
diamond-shaped halfband lowpass filter as the order of the corresponding
BQCW system tends to infinity.
Hence, they are promising in image and multidimensional signal processing
In addition, the synthesis scaling function in a BQCW system of any order is
interpolating (or cardinal), which has been known as a desired merit in
Last Updated 11/07/04.