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Summary: TWO FAMILIES OF SYMMETRY-PRESERVING REVERSIBLE INTEGER-TO-INTEGER
WAVELET TRANSFORMS
Michael D. Adams and Rabab Ward
Dept. of Elec. and Comp. Eng., University of British Columbia, 2356 Main Mall, Vancouver, BC, Canada V6T 1Z4
mdadams@ieee.org and rababw@ece.ubc.ca
ABSTRACT
Two families of symmetry-preserving reversible integer-to-integer
wavelet transforms are introduced. Briefly, we explain how trans-
forms from these families can be used in conjunction with sym-
metric extension in order to handle signals of arbitrary length in a
nonexpansive manner (which is often a desirable attribute in sig-
nal coding applications). The characteristics of the two transform
families and their constituent transforms are then studied. For the
more constrained of the two families, we identify precisely which
transforms belong to the family (by specifying properties and con-
ditions for membership). Such results might be exploited in the fil-
ter bank design process in order to find new symmetry-preserving
reversible integer-to-integer wavelet transforms for signal coding
applications.
1. INTRODUCTION
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