ANZIAM  J.  46 (2004), 111-120
A note on the extension of a family of biorthogonal Coifman wavelet systems

Zhuhan Jiang
  School of Computing and Information Technology
  University of Western Sydney
  Penrith South DC NSW 1797
Xiling Guo
  Management Information Systems
  Australian Catholic University
  Strathfield NSW 2135

Wavelet systems with a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications such as image and video compression. Tian and Wells recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which have proved valuable in both mathematics and applications. The purpose of this work is to establish along with direct proofs a very neat extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other ``missing'' members of the biorthogonal Coifman wavelet systems.
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