The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 4, Issue 9

Preprint: Two preprints on 2D wavelets and filter banks
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Stanhill David (

PostPosted: Fri Dec 06, 2002 9:33 am    
Subject: Preprint: Two preprints on 2D wavelets and filter banks
Reply with quote

Preprint: Two preprints on 2D wavelets and filter banks


Two preprints on 2D wavelets and filter banks are available.
The preprints can be obtained via anonymous ftp to, they are in the directory

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

The compressed file is, and the four figure files are,, and

Title: Two-Dimensional Linear Phase Orthogonal filter-banks and
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, and the two figure files are and

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
Haifa 32000
All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.027022 seconds : 18 queries executed : GZIP compression disabled