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On the Relationship Between the Overlapping Rounding Transform and Lifting Frameworks for Reversible Subband Transforms
 

Summary: 1
On the Relationship Between the Overlapping Rounding Transform and Lifting Frameworks for Reversible
Subband Transforms
Michael D. Adams and Faouzi Kossentini
Abstract
Recently, a new framework for reversible subband transforms based on the overlapping rounding transform (ORT) has been
proposed as an alternative to the lifting framework. In this correspondence, we show that the ORT framework is, in fact, a special
case of the lifting framework with only trivial extensions.
Keywords
Reversible integer­to­integer subband transforms, lifting, overlapped rounding transform.
I. INTRODUCTION
In order to efficiently handle lossless coding in subband coding systems, we require transforms that are invertible in
finite­precision arithmetic. Such transforms are said to be reversible. In [1], Calderbank et al. showed that the lifting
scheme [2] forms an effective framework for constructing reversible transforms. Transforms utilizing this framework
have since found application in numerous coding systems including that of the emerging JPEG­2000 standard [3], [4].
More recently, Jung and Prost [5] have proposed an alternative method for constructing reversible transforms based
on the overlapping rounding transform (ORT). Although the ORT and lifting frameworks appear quite different at first
glance, they are, in fact, intimately related. In what follows, we will show that the ORT framework is, in fact, a special
case of the lifting framework with only trivial extensions.
II. NOTATION AND OTHER PRELIMINARIES

  

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

 

Collections: Engineering