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   -> Volume 4, Issue 9


Preprint: Two preprints on 2D wavelets and filter banks
 
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Stanhill David (davids@techunix.technion.ac.il)
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PostPosted: Fri Dec 06, 2002 9:33 am    
Subject: Preprint: Two preprints on 2D wavelets and filter banks
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Preprint: Two preprints on 2D wavelets and filter banks

Hi

Two preprints on 2D wavelets and filter banks are available.
The preprints can be obtained via anonymous ftp to
ftp.technion.ac.il, they are in the directory
/pub/supported/ee/Signal_processing.

1.
Title: Two-Dimensional Orthogonal Wavelets with vanishing moments.
Authors: David Stanhill & Yehoshua Y. Zeevi .

Abstract: We investigate a very general subset of two-dimensional,
orthogonal, compactly supported wavelets. This subset includes all the
wavelets with a corresponding wavelet (polyphase) matrix that can be
factored as a product of factors of degree-1 in one variable. In this
paper we consider in particular wavelets with vanishing moments. The
number of vanishing moments that can be achieved increases with the
increase of the McMillan degrees of the wavelet matrix. We design
wavelets with the maximal number of vanishing moments for given
McMillan degrees, by solving a set of nonlinear constraints on the
free parameters defining the wavelet matrix, and discuss their
relation to regular, smooth wavelets. Design examples are given for
two fundamental sampling schemes; the quincunx and the four-band
separable sampling. Their relation to the, well known,
one-dimensional Daubechies wavelets with vanishing moments is
discussed.

The compressed file is 2dvm.ps.gz, and the four figure files are
2dvm_fig1.ps.gz, 2dvm_fig2.ps.gz, 2dvm_fig3.ps.gz and 2dvm_fig4.ps.gz.


2.
Title: Two-Dimensional Linear Phase Orthogonal filter-banks and
wavelets.
Authors: David Stanhill & Yehoshua Y. Zeevi .

Abstract: Two-dimensional compactly supported, orthogonal wavelets and
filter-banks having linear phase are presented. Two cases are
discussed, wavelets with two-fold symmetry (centrosymmetric), and
wavelets with four-fold symmetry that are symmetric (or
anti-symmetric) about the vertical and horizontal axes. We show that
imposing the requirement of linear phase in the case of factorable
wavelets, imposes a simple constraint on each of its polynomial
degree-1 factors. We thus obtain a simple and complete method of
constructing orthogonal factorable wavelets with linear phase. This
method is exemplified by design in the case of four-band separable
sampling. An interesting result is obtained, similar to the one well
known in 1D case, orthogonal factorable wavelets can not be both
continuous and have four-fold symmetry.

The compressed file is 2dlp.ps.gz, and the two figure files are
2dlp_fig1.ps.gz and 2dlp_fig2.ps.gz.

I will be more than glad to collaborate with any one who is working
on a 2D application of the DWT and has come to the conclusion that
separable wavelets are not suited for the given application.


David Stanhill
Department of Electrical engineering
Technion,
Haifa 32000
ISRAEL
email: davids@tx.technion.ac.il
All times are GMT + 1 Hour
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