wavelet digest, vol 10, nr 04.txt

现代信号处理讲义,包含许多的例题,解答等Qinghua University publishing house modern signal processing course

http://personal.cityu.edu.hk/~meptse/   


------------------------------


Date: Mon, 1 Oct 2001 11:30:26 +0100
From: "[e-mail]" <[e-mail]>
Subject: #6 Preprint: Matrix Factorizations for Reversible Integer Mapping


Title: Matrix Factorizations for Reversible Integer Mapping
 
Author: Pengwei Hao and Qingyun Shi Center for Information Science
National Laboratory on Machine Perception Peking University Beijing,
100871, China
 
IEEE Transactions on Signal Processing, to appear (2001)


Abstract: Reversible integer mapping is essential for lossless source
coding by transformation. A general matrix factorization theory for
reversible integer mapping of invertible linear transforms is
developed in this paper. Concepts of the integer factor and the
elementary reversible matrix (ERM) for integer mapping are introduced,
and two forms of ERM -- triangular ERM (TERM) and single-row ERM
(SERM) -- are studied. We prove that there exist some approaches to
factorize a matrix into TERMs or SERMs if the transform is invertible
and in a finite dimensional space. The advantages of the integer
implementations of an invertible linear transform are: (i) mapping
integers to integers, (ii) perfect reconstruction, and (iii) in-place
calculation. We find that, besides a possible permutation matrix, the
TERM factorization of an N-by-N nonsingular matrix has at most 3 TERMs
and its SERM factorization has at most N +1 SERMs. The elementary
structure of ERM transforms is the ladder structure. An executable
factorization algorithm is also presented. Then the computational
complexity is compared, and some optimization approaches are
proposed. The error bounds of the integer implementations are
estimated as well. Finally, three ERM factorization examples of DFT,
DCT and DWT are given.


Keywords: Matrix factorization, reversible integer mapping, linear
transforms, lossless compression, lifting scheme


I would be glad to email a PDF copy to anyone that makes a request.
My email address is [e-mail].


Pengwei Hao
 
------------------------------


Date: Tue, 9 Oct 2001 14:12:34 -0600 (MDT)
From: Brandon Whitcher <[e-mail]>
Subject: #7 Preprint: A Wavelet Solution to Spurious Regression


Title:  A Wavelet Solution to the Spurious Regression of Fractionally
        Differenced Processes


Author: Yanqin Fan and Brandon Whitcher


Abstract: In this paper we propose to overcome the problem of spurious
regression between fractionally differenced processes by applying the
discrete wavelet transform (DWT) to both processes and then estimating
the regression in the wavelet domain.  The DWT is known to
approximately decorrelate heavily autocorrelated processes and, unlike
applying a first difference filter, involves a recursive two-step
filtering and downsampling procedure.  We prove the asymptotic
normality of the proposed estimator and demonstrate via simulation its
efficacy in finite samples.


URL:  http://www.cgd.ucar.edu/~whitcher/papers/spurious.pdf


Brandon Whitcher


  Geophysical Statistics Project
  National Center for Atmospheric Research          [phone]  voice
  P.O. Box 3000, Boulder, CO  80307-3000            [phone]  fax


  [e-mail]                            www.cgd.ucar.edu/~whitcher/


------------------------------


Date: Mon, 19 Nov 2001 14:53:33 +0100
From: Thierry BLU <[e-mail]>
Subject: #8 Preprint: Wavelets, Fractals and Radial Basis Functions


The following paper has recently been accepted for publication in the 
IEEE Transactions on Signal Processing. In particular, we give an 
explicit time-domain representation of dyadic wavelets


                          TITLE
      Wavelets, Fractals and Radial Basis Functions


                         AUTHORS
             Thierry BLU and Michael UNSER
    (Swiss Federal Institute of Technology, Lausanne)


                         WEB LINK
            http://bigwww/blu/publis/WRBF.html


                         ABSTRACT
Wavelets and radial basis functions (RBF) lead to two distinct ways of
representing signals in terms of shifted basis functions.  RBFs, unlike
wavelets, are non-local and do not involve any scaling, which makes them
applicable to non-uniform grids.  Despite these fundamental differences, we
show that the two types of representation are closely linked together...
through fractals.  First, we identify and characterize the whole class of
self-similar radial basis functions that can be localized to yield
conventional multiresolution wavelet bases.  Conversely, we prove that, for
any compactly supported scaling function \phi, there exists a one-sided
central basis function \rho that spans the same multiresolution subspaces.
The central property is that the multiresolution bases are generated by
simple translations of \rho, without any dilation.  We also present an
explicit time-domain representation of a scaling function as a sum of
harmonic splines.  The leading term in the decomposition corresponds to the
fractional splines; a recent, continuous-order generalization of the
polynomial splines.
-- 
                         Thierry BLU


   e-mail : [e-mail]
   http://bigwww.epfl.ch/


------------------------------


Date: Wed, 21 Nov 2001 14:51:57 -0800
From: Richard Bartels <[e-mail]>
Subject: #9 Preprint: Reversing subdivision and constructing multiresolutions


#1:
Authors
-------
Bartels, R., Samavati, F.,


Title
-----
Reversing Subdivision Rules:
Local Linear Conditions and
Observations on Inner Products


Appearing in
------------
Journal of Computational and Applied Mathematics 
vol. 119, nos. 1-2, July, 2000, pages 29-67 


Also available at
-----------------
http://www.cgl.uwaterloo.ca/~rhbartel/Papers/LocalLS.pdf
http://pages.cpsc.ucalgary.ca/~samavati/papers/LocalLS.pdf


Abstract
--------
In this work we study biorthogonal systems based upon
subdivision rules and local least squares fitting problems
that reverse the subdivision. We are able to produce
multiresolution structures for some common subdivision
rules that have both finite reconstruction and
decompositions filters. We observe that each biorthogonal
system we produce can be interpreted as a semiorthogonal
system with an inner product induced on the multiresolution
that is quite different from that normally used. Some examples
of the use of this approach on images and geometry are given. 


#2:
Authors
-------
Samavati, F., and Bartels, R. 


Title
-----
Reversing Subdivision Using Local Linear Conditions:
Generating Multiresolutions on Regular Triangular Meshes 


Available at
-----------------
http://www.cgl.uwaterloo.ca/~rhbartel/Papers/TriMesh.pdf
http://pages.cpsc.ucalgary.ca/~samavati/papers/Butterfly.pdf


Abstract
--------
We extended the results of paper #1 to non-tensor-product surfaces
(specifically: regular, triangular-mesh surfaces).
The local matrix approach of #1 is replaced by an approach based upon
masks.
To demonstrate the generality of the approach, examples of finite
multiresolution
filters are generated for Butterfly and Loop subdivision and for
a subdivision recently proposed by Litke, Schroeder, et al.


Richard Bartels
University of Waterloo
Waterloo, Ontario
Canada


Faramarz Samavati
University of Calgary
Calgary, Alberta
Canada


------------------------------


Date: Wed, 3 Oct 2001 16:08:28 -0500 
From: "Fernandes, Felix" <[e-mail]>
Subject: #10 Thesis: Complex Wavelet Transforms with Controllable Redundancy


My Ph.D. dissertation entitled 


Directional, Shift-Insensitive, Complex Wavelet Transforms with
Controllable Redundancy


is available at 


http://www.ece.rice.edu/~felixf/dissertation.ps


Felix Fernandes.


Abstract: Although the Discrete Wavelet Transform (DWT) is a powerful
tool for signal and image processing, it has three serious
disadvantages.  First, the DWT is shift sensitive because input-signal
shifts generate unpredictable changes in DWT coefficients.  Second,
the DWT suffers from poor directionality because DWT coefficients
reveal only three spatial orientations.  Third, DWT analysis lacks the
phase information that accurately describes non-stationary signal
behavior.  To overcome these disadvantages, we introduce the notion of
projection-based complex wavelet transforms.


These two-stage, projection-based complex wavelet transforms consist
of a projection onto a complex function space followed by a DWT of the
complex projection. Unlike other popular transforms that also mitigate
DWT shortcomings, the decoupled implementation of our transforms has
two important advantages. First, the controllable redundancy of the
projection stage offers a balance between degree of shift sensitivity
and transform redundancy.  This allows us to create a directional,
non-redundant, complex wavelet transform with potential benefits for
image coding systems.  To the best of our knowledge, no other complex
wavelet transform is simultaneously directional and non-redundant.
The second advantage of our approach is the flexibility to use
\emph{any} DWT in the transform implementation. We exploit this
flexibility to create the Complex Double-density DWT (CDDWT): a
shift-insensitive, directional, complex wavelet transform with a low
redundancy of $\frac{3^m - 1}{2^m - 1}$ in $m$ dimensions. To the best
of our knowledge, no other transform achieves all these properties at
a lower redundancy.  Besides the mitigation of DWT shortcomings, our
transforms have unique properties that will potentially benefit a
variety of signal processing applications. As an example, we
demonstrate that our projection-based complex wavelet transforms
achieve state-of-the-art results in a seismic signal-processing
application.


------------------------------


Date: Thu, 1 Jan 1998 00:59:45 +0100
From: "Rimvydas Aleksiejunas" <[e-mail]>
Subject: #11 Software: Joint time-frequency analysis using Signalogram


The Signalogram is a PC-based software package for signal and image
visualization and analysis. It includes data wrapper classes, algorithm
management system and graphical user interface (GUI). The GUI is written for
MS Windows platforms. Such an interface enables analysis of several data
sets simultaneously, multithreading, representation of results by tables,
1D, 2D and 3D plots as well as error messaging.


The software is designed as a set of separate modules prepared using
templates and linked to the main application by means of COM technology. One
of the modules is devoted to the joint time-frequency analysis, namely, the
short-time Fourier transform, which is calculated using the discrete Gabor
transform and the discrete Zak transform according to the paper:


M. J. Bastiaans and M. C. W. Geilen, On the discrete Gabor transform and the
discrete Zak transform, Signal Process. 49 (1996), 151-166.


The package is available at:


 http://signalogram.free-hosting.lt
or
 http://signalogram.tinklapis.lt


Rimvydas Aleksiejunas
Dept. Radiophysics
Vilnius University
Sauletekio al. 9 k. 3
LT-2040 Vilnius, Lithuania
Email: [e-mail]


------------------------------


Date: Mon, 1 Oct 2001 14:02:45 GMT
From: [e-mail]
Subject: #12 Meeting: Third Seminar Wavelets and their Applications


           Third Seminar "Wavelets and their Applications"


In the framework of the NWO research project "Wavelets and their
Applications" in which CWI, RUG, TUE and UT participate, a general
seminar dealing with various aspects of theoretical and applied
aspects of wavelets and related areas, will be organised twice a year
(May/June and November/December).  Each meeting will consist of two
parts.  The morning session consists of an invited two-hour lecture by
one of the leading experts in wavelet theory.  The afternoon session,
comprising two or three lectures will be devoted to various topics.


The next meeting will be held on the 23rd of November 2001 at the
University of Eindhoven, Netherlands.  Main speaker is


                     Wolfgang Dahmen from Aachen.


The full programme will be announced on the following website:


                 http://www.cwi.nl/projects/wavelets/


There one can also find other information concerning the NWO project
and the seminar and fill out a registration form (note that
registration is free of charge).  Further information can also be
obtained from Hennie ter Morsche ([e-mail]) or Lute Kamstra
([e-mail]).


Lute Kamstra
CWI department PNA4
Office M233
email: [e-mail]                    phone: [phone]


------------------------------


Date: Thu, 18 Oct 2001 09:33:20 +0900