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   -> Volume 7, Issue 2

Preprint: Multiwavelets (Analysis, Construction, and Compression)
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Tham Jo Yew (

PostPosted: Wed Feb 11, 1998 9:54 am    
Subject: Preprint: Multiwavelets (Analysis, Construction, and Compression)
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#7 Preprint: Multiwavelets (Analysis, Construction, and Compression)

We would like to announce the availability of the following series of
3 papers pertaining to the analysis, construction and application of
discrete multiwavelets to image compression:

1. Title: A General Approach for Analysis and Application of Discrete
Multiwavelet Transforms
Authors: Jo Yew Tham, Lixin Shen, Seng Luan Lee, and Hwee Huat Tan
Status: Submitted for publication (Sept. 1997)

In this paper, we propose a general approach for the analysis and
application of discrete multiwavelet transforms to image compression.
First, we establish a relationship between a given multiwavelet system
and its equivalent scalar (wavelet) filter bank system. We then
propose a new measure called the {it good multifilter properties}
(GMPs), which is a tool to analyze whether a given multiwavelet system
is ``good" in terms of having desirable filter characteristics.
Second, we propose a generalized framework for the application of any
multiwavelet systems to image compression. A simple, orthogonal and
non-redundant pre-analysis and post-synthesis multirate filtering
technique is proposed. In order to investigate the significance and
effectiveness of our proposals, we performed a series of simulation
tests using both scalar and multiwavelets. Our simulations show that
a length-4 orthogonal multiwavelet filter satisfying the proposed
GMPs, and using the proposed initialization technique, not only have
lower computational complexity than the length-4 Daubechies scalar
wavelet (D4) but also outperforms the length-8 Daubechies wavelet (D8)
and other length-4 orthogonal multiwavelets.

image compression, wavelets, multiwavelets, pre-analysis
and post-synthesis filtering, good multifilter properties.

2. Title: A New Class of Orthogonal Multiwavelets for Image
Authors: Lixin Shen, Jo Yew, and Hwee Huat Tan
Status: Submitted for publication (Sept. 1997)

A new class of symmetric-antisymmetric orthogonal multiwavelets
(SAOMWs) for applications in image compression is introduced. We first
review the definitions of {it good multifilter properties} (GMPs),
which were established in an earlier exposition. There, we also showed
how a multifilter possessing GMPs can give improved image compression
performances. The main objective of this paper is to further extend
the above concepts by constructing a new class of SAOMWs which
satisfies all the GMPs simultaneously. A thorough investigation in
terms of frequency characteristics as well as the relation between
even-length and odd-length multifilters are carried out. Then, we
provide an explicit formulation for the construction of matrix
highpass filters directly from the corresponding matrix lowpass
filter, and present a procedure for the construction of this class of
multifilters. Finally, our simulation tests confirm the importance of
GMPs, and show how a length-4 member of this class of SAOMWs can have
a lower computational complexity, but still outperforms other
orthogonal multiwavelets of equal filter length, and the scalar 4-tap
and 8-tap Daubechies wavelets.

image compression, wavelets, multiwavelets, orthogonality,
linear phase, good multifilter properties.

3. Title: Symmetric-Antisymmetric Orthonormal Multiwavelets
and Related Scalar Wavelets
Authors: Lixin Shen, Hwee Huat Tan, and Jo Yew Tham
Status: Submitted for publication (Dec. 1997)

For compactly supported symmetric-antisymmetric orthonormal
multiwavelets with multiplicity 2, we first show that any length-2N
multiwavelet can be constructed from length-(2N+1) multiwavelet, and
vice versa. Then we present two explicit formulations for the
construction of multiwavelet functions directly from their associated
multiscaling functions. Lastly, we establish the relationship between
these multiwavelets and their related orthonormal scalar wavelets, and
construct two families of symmetric-antisymmetric orthonormal
multiwavelets via the construction of the related scalar wavelets.

orthonormal multiwavelets, scalar wavelets.

The pre-prints (both postscripts and ZIP compressed versions) can be
obtained from:
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