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SYMMETRY-PRESERVING REVERSIBLE INTEGER-TO-INTEGER WAVELET Michael D. Adams and Rabab Ward
 

Summary: 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
Studied are two lifting-based families of symmetry-preserving re-
versible integer-to-integer wavelet transforms. The transforms from
both of these families are shown to be compatible with symmet-
ric extension, which permits the treatment of arbitrary length sig-
nals in a nonexpansive manner. Throughout this work, particularly
close attention is paid to rounding functions, and the properties
that they must possess in various instances. Symmetric extension
is also shown to be equivalent to constant per-lifting-step extension
in certain circumstances.
1. INTRODUCTION
Lifting-based reversible integer-to-integer wavelet transforms [1,
2] have become a popular tool in signal coding applications. In
such applications, however, it is often desirable to employ trans-
forms that preserve symmetry. For example, symmetry-preserving

  

Source: Adams, Michael D. - Department of Electrical and Computer Engineering, University of Victoria

 

Collections: Engineering