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Wavelet Digest, Vol. 4, Nr. 5.
Wavelet Digest Tuesday, May 2, 1995 Volume 4 : Issue 5
Today's Editor: Wim Sweldens
University of South Carolina
sweldens@math.scarolina.edu
Today's Topics:
1. Preprint: Image Features From Phase Congruency
2. Preprint: Optimal Matched Wavelet Construction...
3. Preprint: Fast Wavelet Based Volume Rendering by Accumulation...
4. Preprint: A New Method to Approximate the Volume Rendering Equation...
5. Preprint: Multiscale decompositions on bounded domains
6. Software: Wavelet Toolbox for Khoros2.0
7. Software: Wavelet Toolbox for Matlab (Version 1.0)
8. Meeting: Digital Video Compression 1996 San Jose
9. Meeting: New advances in biomedical signal and image processing
10. Job: Opening for Research Scientist: Wavelets
11. Contents: Advances in Computational Mathematics
12. Answer: Derivatives of wavelets (WD 4.4 #14)
13. Answer: Frequency Modulation Laws (WD 4.4 #15)
14. Answer: Reference missing in Daubechies' Ten lectures ?
15. Question: How to obtain Paper on Connection Coefficients.
16. Question: Application of wavelets to fractal signals.
19. Question: Truncated sequences for B-spline wavelet.
18. Question: Looking for code with non power of 2 length signals
19. Question: Triadic Haar wavelets problem
20. Internet: A newly released WWW server : INRIA Fractales Project.
Submissions:
E-mail to wavelet@math.scarolina.edu with "submit" as subject.
Subscriptions:
E-mail to wavelet@math.scarolina.edu with "subscribe" as subject.
To unsubscribe, e-mail with "unsubscribe" followed by your e-mail
address as subject. To change address, unsubscribe and resubscribe.
Preprints, references, and back issues can be obtained from our
information servers:
Ftp: ftp.math.scarolina.edu (/pub/wavelet)
Gopher: gopher.math.scarolina.edu
WWW: <A HREF="http://www.math.scarolina.edu/~wavelet/">Here</A>
Current number of subscribers: 4567
Calendar of events:
May 17-20: Course: Wavelets: Principles, Applic. and Implement. WD 4.2 #17
May 22-24: Course: Fuzzy Logic, Chaos, and Neural Networks, UCLA WD 4.2 #15
May 30-Jun 3: Meeting of the Acoustical Society of America, DC WD 4.1 #7
Jun 6-8 : Mathematics and Physics of Wavelets, College Park MD WD 4.4 #12
Jun 26-30: ANU Wavelets Workshop, Canberra, Australia WD 3.6 #6
Jul 3-7 : SIAM ICIAM 95, Hamburg, Germany WD 3.19 #15
Jul 8-17: Fractal Image Encoding and Analysis, Trontheim, Norway WD 4.4 #10
Jul 13-14: SPIE: Mathematical Imaging: San Diego WD 4.1 #6
Jul 24-28: Wavelets in Electromagnetics PIERS, Seattle WD 3.18 #11
Jul 31-Aug 25: International Summer School, Jyvaskyla, Finland WD 4.3 #12
Aug 31-Sep 1: UK Symp. on Time-Freq. and Time-Scale, Warwick UK WD 4.3 #10
Sep 17-21: ASME Wavelets in Vibrations and Acoustics, Boston WD 3.17 #11
*Sep 20-23: Advances In Biomedical Signal And Image Proc, Monteal WD 4.5 #9
Dec 10-13: Neural Networks and Signal Processing, Nanjing, China WD 4.3 #9
-- 1996 --
*Jan 28-Feb 2: Digital Video Compression, San Jose, CA WD 4.5 $8
--------------------------- Topic #1 -----------------------------------
From: Peter Kovesi <Peter.Kovesi@sophia.inria.fr>
Subject: Preprint: Image Features From Phase Congruency
Technical Report Available by anonymous ftp from
cs.uwa.edu.au /pub/techreports/95/4.ps.gz
Title: Image Features From Phase Congruency
Author: Peter Kovesi
Department of Computer Science
The University of Western Australia
Nedlands, W.A. 6009
email: pk@cs.uwa.oz.au
Abstract: Image features such as step edges, lines and Mach bands all
give rise to points where the Fourier components of the image are
maximally in phase. The use of phase congruency for marking features
has significant advantages over gradient based methods. It is a
dimensionless quantity that is invariant to changes in image
brightness or contrast, hence it provides an absolute measure of the
significance of feature points. This allows the use of universal
threshold values that can be applied over wide classes of images.
This paper presents a new way of calculating phase congruency through
the use of wavelets. The existing theory that has been developed for
1D signals is extended to allow the calculation of phase congruency in
2D images. It is shown that for good localization it is important to
consider the spread of frequencies present at a point of phase
congruency. An effective method for identifying, and compensating
for, the level of noise in an image is presented. Finally, it is
argued that high-pass filtering should be used to obtain image
information at different scales. With this approach the choice of
scale only affects the relative significance of features without
degrading their localization.
--------------------------- Topic #2 -----------------------------------
From: joc8048@borg.cis.rit.edu (Joe Chapa)
Subject: Preprint: Optimal Matched Wavelet Construction...
Title: Optimal Matched Wavelet Construction and Its
Application to Image Pattern Recognition
Authors: Joseph O. Chapa, Maj, USAF
Center for Imaging Science
Rochester Institute of Technology
Rochester, NY
Mysore R. Raghuveer
Dept. of Electrical Engineering
Rochester Institute of Technology
Rochester, NY
Presented At: Conference on Wavelet Applications for Dual Use
SPIE's 1995 Symposium on OE/Aerospace Sensing
and Dual Use Photonics
Make all requests via e-mail to: joc8048@borg.cis.rit.edu
Abstract:
Wavelet transforms applied to multiresolution analyses of
images produce outputs similar in theory to those of matched
filters. In order to maximize the outputat the location and
scale of a signal of interest, it is necessary for the wavelet used
in the multiresolution analysis to ``match'' the signal of interest.
Current techniques match a signal to one of several predefined
wavelets in a library, which requires wavelets to be designed in
advance. Here, we present an alternative by developing a
technique for deriving a bandlimited wavelet directly from the
desired signal spectrum in such a way that the mean squared error
between their spectra is a minimum. Furthermore, the matched
wavelet is designed such that its associated scaling function
generates an orthonormal multiresolution analysis. The technique
includes an algorithm for finding the scaling function from an
orthonormal wavelet, and algorithms for finding the optimal
wavelet magnitude and phase from a given input signal. Two
examples are shown to demonstrate the performance of the
technique for both known orthonormal wavelets and arbitrary signals.
{\bf Keywords:} wavelet construction, bandlimited wavelets,
matched wavelet, pattern recognition.
--------------------------- Topic #3 -----------------------------------
From: Lars Lippert <lippert@inf.ethz.ch>
Subject: Preprint: Fast Wavelet Based Volume Rendering by Accumulation...
Title: Fast Wavelet Based Volume Rendering by
Accumulation of Transparent Texture Maps
Preprint & figures available by anonymous ftp from ftp.inf.ethz.ch
Directory: /doc/tech-reports/1995
Report-No: 228
Authors: L. Lippert, M. H. Gross
Abstract:
In the this paper, a new method for fast and accurate volume
intensity and color integration is elaborated, which employs
wavelet decompositions and texture mapping. At this point,
it comprises and unifies the advantages of recently
introduced Fourier domain volume rendering techniques and
wavelet based volume rendering. Specifically, the method
computes analytic solutions of the ray intensity integral
through a single wavelet by slicing its Fourier transform
and by backprojecting it into the spatial domain. The
resulting slices can be considered as RGB textures where R,
G and B account for the decomposed volume color function.
Due to the similarity of the basis functions, the
computation of the texture map has to be figured out only
once for each 3D mother wavelet. Hence, the final volume
rendering procedure turns out to be a superposition of self-
similar, transparent and colored textures, which is
supported by modern hardware accumulation buffers. Linear
shading and attenuation can be introduced by modifications
of the wavelet's Fourier transform.
The main advantages of this method are the provision of accu-
rate solutions and quantification of error bounds, the ab
sence of any expensive prefiltering and the independence of
the computational costs from the image resolution. Further
more, any required discretization, such as the resolution of
the basis textures is defined within the computational frame
work of the wavelet transform. The method is not restricted
to a specific type of wavelet unless is provides an analytic
Fourier description, such as any B-spline wavelets do.
anonymous ftp://ftp.inf.ethz.ch/doc/tech-reports/1995
Lars Lippert, Computer Graphics Research Group, Institute for
Information Systems Swiss Federal Institute of Technology Zuerich,
Tel.: +41-1-632 71 21, Email: lippert@inf.ethz.ch, Fax : +41-1-632 11 72
http://www.inf.ethz.ch/department/IS/cg/
--------------------------- Topic #4 -----------------------------------
From: Lars Lippert <lippert@inf.ethz.ch>
Subject: Preprint: A New Method to Approximate the Volume Rendering Equation...
Title: A New Method to Approximate the Volume
Rendering Equation using Wavelet Bases
and Piecewise Polynomials
Preprint & figures available by anonymous ftp from ftp.inf.ethz.ch
Directory: /doc/tech-reports/1994
Report-No: 220
Authors: M. Gross, L. Lippert, A. Dreger, R. Koch
Abstract:
In this paper we describe a new generic method to find an approximate
solution for the volume rendering equation using hierarchical, orthonormal
wavelet basis functions. The approach is based on the idea that an initial
volume data set can be decomposed into a pyramidal representation by means
of a 3D wavelet transform. Once the wavelet function is described analytically,
it is possible to approximate the volume density function. Moreover, when
employing piecewise polynomial spline functions, as in our method, the
rendering integral can also be approximated and gradient functions or related
features of the data can be computed immediately from the approximation.
Due to the localization properies of the wavelet transform both in space and
in frequency on the one side and due to the pyramidal subband coding scheme on
the other side, this technique allows additionally for the control of the local
quality of the reconstruction and provides elegantly for level-of-detail
operations.
Aside from the solution of the rendering equation itself, isosurfaces of the
data can also be computed with either standard techniques, like marching cubes,
or by more sophisticated algorithms that render the basis functions. All these
additional rendering techniques can be embedded in a hybrid surface/volume
rendering scheme. In our paper, we elucidate this new concept and show its
capabilities by different examples.
anonymous ftp://ftp.inf.ethz.ch/doc/tech-reports/1994
--------------------------- Topic #5 -----------------------------------
From: dahmen@igpm.rwth-aachen.de (Wolfgang Dahmen)
Subject: Preprint: Multiscale decompositions on bounded domains
The manuscript ``Multiscale decompositions on bounded domains''
by A. Cohen, W. Dahmen, R. DeVore is available as a (compressed) postscript
file by anonymous ftp under cdd.ps.Z
apply the following procedure:
ftp ftp.igpm.rwth-aachen.de
login: anonymous
use e-mail address as password
cd reports
bin
get cdd.ps.Z
after receiving uncompress the file
--------------------------- Topic #6 -----------------------------------
From: nuria@tsc.uvigo.es (Nuria Gonzalez Prelcic )
Subject: Software: Wavelet Toolbox for Khoros2.0
Uvi_Wave Pre-release
WAVELET TOOLBOX for KHOROS2.0
A Pre-release of the Uvi_Wave Wavelets toolbox for Khoros 2.0 is
available via anonymous ftp from:
ftp.tsc.uvigo.es:/pub/Uvi_Wave/khoros2/
or
ftp.cesga.es:/pub/Uvi_Wave/khoros2/
This new software is still being developed. Comments, suggestions and
bug reports will be greatly appreciated. The mail address for reports is
Uvi_Wave@tsc.uvigo.es
The programs included in the toolbox are :
(A more extensive repport will be included in the ftp server)
MAIN PROGRAMS:
* KMWT: The Multilevel Wavelet Transform. Supports the multiscale
(different
number of scales for each direction) feature and fast matricial
computations have been included.
kmwt supports the following tasks:
- The multilevel Direct and Inverse Wavelet
Transform. With variable
number of scales for each dimension, as
extended options.
- Incomplete Inverse transform for multirresolution
analysis purposes.
* kwtband : It's a program which supports up to 8 subband
utilities: extraction,
insertion, normalization, location, ....
kwtband supports the following tasks:
- Subband Normalization for viewing.
- Subband Extraction-Insertion routines (different options for
insertion).
- Subband Location Change.
- Subband Localization.
* kwwavscl : The program that calculates the Wavelet and Scale functions.
kwwavscl supports the following tasks:
- Wavelet Function generation.
- Scale Function generation.
* kwtfilter : The Filter Generator.
kwtfilter supports the following tasks:
- Generation of Daubechies Orthogonal filters.
- Generation of Spline Biorthogonal filters.
* kwmres : The Multiresolution Analysis module. Computes approximations and
details from objects.
kwmres supports the following tasks:
- Calculation of any approximation or detail of any
object, where the band selection is made independently
by directions.
OTHER FILES:
* Other pane programs: The above programs have been provided with several
pane files with different levels of complexity according to the
user's needs.
* Library routines: The toolbox library holds a bunch of little aid
routines for coordinate and size calculation, scale checking,
and others.
We hope this will help about the toolbox structure. You may try the
Matlab version of the toolbox, available at the same site.
Sergio J. Garcia Galan E-mail: Uvi_Wave@tsc.uvigo.es
Nuria Gonzalez Prelcic
Departamento de Tecnologias de las Comunicaciones
Universidad de Vigo
SPAIN
--------------------------- Topic #7 -----------------------------------
From: nuria@tsc.uvigo.es (Nuria Gonzalez Prelcic )
Subject: Software: Wavelet Toolbox for Matlab (Version 1.0)
Uvi_Wave version 1.0
WAVELET TOOLBOX for MATLAB
I am pleased to announce you the Wavelet Toolbox for Matlab called "Uvi_Wave".
It is available by anonymous ftp at the following sites:
ftp.tsc.uvigo.es
(directory: pub/Uvi_Wave/matlab/)
or
ftp.cesga.es
(directory: pub/Uvi_Wave/matlab/)
This Wavelet Toolbox for Matlab intends to help the researches and education
professionals interested on any of the possibilities that Wavelet Processing
offers. We hope the tools developed into a widely used environment as Matlab,
can be useful for the scientific community.
In the next paragraphs, a short description of the main features of the
Uvi_Wave Toolbox can be found.
* Discrete Wavelet Transform: calculation and visualization of the Discrete
Wavelet Transform (DWT) and Inverse Discrete Wavelet Transform (IDWT) for an
unidimensional or bidimensional signal. No restrictions on signal length.
* Scale Function and Wavelet Function: calculation and visualization of
the discrete approximation to the scale and wavelet functions, obtained
from the cascade algorithm.
* Multiresolution analysis: the objective of these routines is the
representation of the information into a set of approximation signals
and detail signals at different resolutions.
* Non subsampled filter bank: the routines that implement this structure
can be useful for singularity detection.
* Wavelet design: design of a set of filters that lead to the wavelet
decomposition and reconstruction. The selected design algorithms includes
orthogonal (Daubechies filters) and biorthogonal (Spline solution) families.
In addition some demos and utilities for subband managing and viewing
have been included.
Despite the functions are clearly commented, we are working on the
documentation. We are also finishing a second version that includes
functions to work with wavelet packets, other filter generation algorithms
and some tools to analyze filter regularity.
Comments, suggestions and bug reports will be greatly appreciated. The mail
address for any question or comment is :
Uvi_Wave@tsc.uvigo.es
Nuria Gonzalez Prelcic
Sergio J. Garcia Galan
Departamento de Tecnologias de las Comunicaciones
Universidad de Vigo
SPAIN
--------------------------- Topic #8 -----------------------------------
From: panch@trix.genie.uottawa.ca
Subject: Meeting: Digital Video Compression 1996 San Jose
Digital Video Compression: Algorithms and Technologies 1996
(IS&T/SPIE Symposium On Electronic Imaging: Science and Technology),
Jan. 28 - Feb. 2, 1996, The SanJose Convention Center, SanJose, California.
Chairs: Bhaskaran Vasudev, Hewlett-Packard Laboratories;
Frans Sijstermans, Philips Research Laboratories;
Sethuraman Panchanathan, University of Ottawa;
Committee: Andrew Lippman, MIT Media Lab;
Ephraim Feig, IBM T.J. Watson Research Ctr.;
Eric Viscito, Chromatic Research Corp.;
James Normile, Apple Computer;
K. R. Rao, Univ. of Texas/Arlington;
King Ngan, Univ. of Western Australia(Australia);
V. Michael Bove, Jr.; MIT Media Lab;
Michael Orchard, Univ. of Illinois/Urbana-Champaign;
Riccardo Leonardi, Univ. of Brescia(Italy);
Robert Safranek, AT&T Bell Labs;
Shiv Balakrishnan, Philips Semiconductor Corp.;
Stefan Eckhart, Chromatic Research Corp.;
Subramania I. Sudharsanan, Digital Equipment Corp.;
Svetha Venkatesh, Curtin Univ. of Tech.(Australia);
Touradj Ebrahimi, EPFL, Lausanne (Switzerland);
Advances in computer and network technologies and the
availability of large-capacity storage devices have significantly
advanced multimedia capabilities of computer platforms and
consumer devices. The need to support digital video within this
multimedia environment imposes significant demands on such
multimedia systems. Technologies such as video compression are
therefore critical in such systems.
This conference brings together practitioners and researchers
working in all aspects of digital video. The conference will
serve as a forum for exchange of novel ideas on video
compression research, codec development, hardware and software
implementations. Presenters will be encouraged to demonstrate
their digital video solutions. Also encouraged are
presentations on the underlying concepts behind these
technologies and the compromises required when implementing such
technologies within real-world resource constraints.
Papers are solicited in all areas of digital video and audio
codec methods, including, but not limited to:
* basic video coding algorithms (DCT based, fractals, etc.)
* scalable video coding schemes (wavelets, sub-band, pyramids)
* motion-estimation techniques
* bitrate control issues and implementations
* pre and post processing for video compression
* MPEG, H.261 standards related video coding methods
(algorithms, implementations, software-only solutions)
* software-only video coder implementations
* special hardware implementations (VLSI, DSP, parallel processor)
* very low bit rate video coding techniques including H.26P
* morphological and model based coding methods
* video coding for wireless and mobile applications
* combined source-channel coding
* error concealment methods
* video scene content analysis in compressed and uncompressed
domain
* perceptual quality quantification
* audio compression methods
Papers describing case studies of digital video codec algorithms,
technologies and system integration issues are also welcome.
Each paper will be reviewed by members of the program committee.
Please submit a 5-10 page, double-spaced summary for review on
July 3, 1995 along with your abstract.
To qualify for Acceptance:
- send 500 word abstract of paper and 5-10 page double spaced summary
in one of following ways:
a) electronic mail to abstracts@mom.spie.org
b) fax to SPIE at 306-647-1445, or
c) mail (send 4 copies) to
IS&T/SPIE EI'96
SPIE P.O. Box 10, Bellingham, WA 98225, USA
Tel: 360-676-3290, Fax: 360-647-1445
Your abstract should include the following:
a) Title of paper
b) Authors' listing - full names and affiliations as they will appear in
the program.
c) Correspondence for each author - complete address, telephone, fax no.,
email address
d) Submit to: indicate conference title as
Digital Video Compression: Algorithms and Technologies 1996
indicate conference chair as
Vasudev Bhaskaran or Frans Sijstermans or
Sethuraman Panchanathan
e) The key words that best describe the subject of my work are: ......
f) Abstract text: 500 words
g) Brief biography: 50-100 words (principal author only)
- applicants will be notified of acceptance by Oct. 28, 1995.
- full manuscript for the conference proceedings must be submitted by
Jan. 2, 1996.
IMPORTANT NOTE: As of March 10, my telephone number changes to
(613)-562-5800 x6206 , and the FAX number becomes +1-613-562 5175.
S. Panchanatha, Associate Professor, Multimedia Communications
Research Laboratory, Department of Electrical Engineering, University
of Ottawa, Ottawa, Ontario,Canada : K1N 6N5, email :
panch@elg.uottawa.ca, panch@trix.genie.uottawa.ca, Phone :
(613)-562-5800 Extn. 6206, Fax : (613)-562-5175
--------------------------- Topic #9 -----------------------------------
From: Bill Thompson <wgthom@gandalf.rutgers.edu>
Subject: Meeting: New advances in biomedical signal and image processing
Dear Colleague:
In the upcoming International Conference of the IEEE Engineering in
Medicine and Biology Society (EMBS) in Montreal, September 20-23, 1995, a
1 1/2 days workshop on NEW ADVANCES IN BIOMEDICAL SIGNAL AND IMAGE PROCESSING
will be held before the conference to discuss and present new advances in
biomedical signal and image processing methods and recent applications
of these emerging technologies including Time-Frequency, Wavelet Transform,
and Wavelet Packets.
I am pleased to invite you to join us for these exciting presentations
by prominent experts in engineering, medicine, computer science and
applied mathematics.
The cost for each attendee will be:
1. $100 for IEEE student member
2. $200 IEEE members,
3. $300 non IEEE members.
If you are interested in joining us at Montreal, and have any
questions about the workshop and registrations, please contact me
at Rutgers (908-445-4096) or e-mail (akay@gandalf.rutgers.edu).
Sincerely,
Metin Akay, Ph.D.
Workshop Chair
17th Annual International Conference of IEEE EMBS
WORKSHOP
NEW ADVANCES IN BIOMEDICAL SIGNAL AND IMAGE PROCESSING
Time-Frequency, Wavelets, Wavelet Packets in Biomedical Engineering
Organizing Committee
Tom Brotherton Patrick Flandrin Dennis Healy Andrew Laine
Mohsine Karrakchou Yves Meyer Janet Rutledge Banu Onaral
Tim Olson Malvin Teich Ahmed Tewfik Nitish Thakor
Michael Unser Victor Wickerhaus William Williams Andrew Yagle
In this workshop, we will focus on the tutorial presentations of advanced
signal and image processing methods. These will include new advances in
time-frequency and wavelet transform and wavelet packets.
In addition, biomedical and image processing applications will
be presented. The invited speakers are experts in the areas of signal
processing, medical imaging, computers science and applied mathematics.
We encourage engineers, medical researchers, computers scientists and applied
mathematicians to learn about recent developments in signal and image
processing and their applications in biomedical engineering.
FUTURE TOPICS AND INVITED SPEAKERS
1. Time-Frequency and Wavelets in Signal and Image Processing:
Algorithms and Implementations
Yves Meyer
2. The generalized sampling and the design of discrete/continuous signal
processing algorithms
Michael Unser
3. The survey of the time-frequency analysis method from Wigner to
the Modern approaches
William Williams
4. The recent advances in quadratic time-frequency analysis methods
Patrick Flandrin
5. Epileptic Seizure Detection Based on Wavelet Analysis of EEG
Banu Onaral
6. Wavelet and Point-Process Analysis of Fractal Neural Firing Patterns
in Audition and Vision
Malvin Teich
7. Modern Methods in Neurological Signal Processing
Applications to Detection of Brain Injury
Nitish Thakor
8. Wavelets and Neural Networks in Maturation
Metin Akay
9. The adapted waveform de-noising for medical signals and images
Victor Wickerhauser
10. The noise reductions and spectral shaping as a combined processing
strategy for hearing aids
Janet Rutledge
11. New Signal Processing Techniques for Physiological Data Analysis
Mohsine Karrakchou
12. Multiscale wavelet frames for contrast enhancement of digital radiographs
Andrew Laine
13. Waveform and beamform design for range and 2-D Doppler ultrasound imaging
Ahmed Tewfik
14. Reducing the imaging time in MRI
Dennis Healy
15. Non-linear stabilization of ill-conditioned linear
inverse problems via adaptive subspace decomposition
Tim Olson
16. Inversion of the radon transform under wavelet constraints
Andrew Yagle
17. The Application of Wavelets and Fuzzy Logic Based Neural Nets to
Medical Data and Image Processing Problems
Tom Brotherton
---
Note from the editor: For the abstracts, please contact the organizers
directly. They were too large to fit into the digest.
--------------------------- Topic #10 -----------------------------------
From: andrew@statsci.com (Andrew Bruce)
Subject: Job: Opening for Research Scientist: Wavelets
Job Opening for Research Scientist: Wavelets
The ideal candidate is self motivated and independent, has 3+
years experience in contract research, and works well in a
team oriented R&D environment. Ability to take a leadership role
in establishing directions and obtaining funding for research
and development of wavelet, and related signal processing methods.
This invididual is also to be responsible for designing wavelet
courses and other educational material. Good written communication
skills and software engineering skills are essential. A Phd in
engineering, statistics, math, CS, or other quantitative discipline
and prior research experience in the theory and application of wavelets,
or a closely related discipline, is required.
StatSci is the premier supplier of object-oriented data analysis
and visualization software. We have an intellectual, small company
atmosphere, have rapidly grown over the last 5 years, and have
aggressive growth plans for the future.
Please send, fax or E-mail your resume to:
Human resources,
Statistical Sciences Division,
MathSoft, Inc.,
1700 Westlake Ave. N., Suite 500,
Seattle, WA 98109.
FAX: (206) 283-6310,
E-mail: hr@statsci.com
--------------------------- Topic #11 -----------------------------------
From: publish@baltzer.nl (Baltzer Science Publishers)
Subject: Contents: Advances in Computational Mathematics
CONTENTS:
Advances in Computational Mathematics, Volume 3, No. III, 1995, ISSN 1019
7168 Editors-in-Chief: John C. Mason & Charles A. Micchelli
Advances in Computational Mathematics is an interdisciplinary journal of
high quality, driven by the computational revolution and emphasising
innovation, application and practicality.
This journal is of interest to a wide audience of mathematicians,
scientists and engineers concerned with the development of mathematical
principles and practical issues in computational mathematics.
Volume 3, No. III, 1995
pp. 171-196: C.T.H. Baker, C.A.H. Paul and D.R. Wille, Issues in the
numerical solution of evolutionary delay differential equations
pp. 197-218: S. Noelle, Convergence of higher order finite volume schemes
on irregular grids
pp. 219-238: T. Sauer, Computational aspects of multivariate polynomial
interpolation
pp. 239-250: M. Gasca and J.M. Pena, On the characterization of almost
strictly totally positive matrices
pp. 251-264: R. Schaback, Error estimates and condition numbers for radial
basis function interpolation
pp. 265-290: J.W. Jones and B.D. Welfert, Zero-free regions for a rational
function with applications
pp. 291-308: K. Strom, B-splines with homogenized knots
Submissions of articles and proposals for special issues are to be
addressed to the Editors-in-Chief:
John C. Mason
School of Computing and Mathematics, University of Huddersfield,
Queensgate, Hudersfield, HD1 3DH, United Kingdom
E-mail: j.c.mason@hud.ac.uk
or
Charles A. Micchelli
Mathematical Sciences Department
IBM Research Center
P.O. Box 218, Yorktown Heights, NY 10598, USA E-mail: cam@yktvmz.bitnet
Requests for FREE SPECIMEN copies and orders for Advances in Computational
Mathematics are to be sent to: E-mail: publish@baltzer.nl
--------------------------- Topic #12 -----------------------------------
From: Mitch Oslick <mho@nova1.stanford.edu>
Subject: Answer: Derivatives of wavelets (WD 4.4 #14)
In volume 4, no. 4 of the Wavelet Digest, Tony Cai asked about computing the
derivatives of scaling and wavelet functions associated with multiresolution
analyses (specifically, Daubechies' orthonormal wavelets and coiflets). The
answer is found in two papers by Daubechies and Lagarias: "Two-Scale Difference
Equations I. Existence and Global Regularity of Solutions" and "Two-Scale
Difference Equations II. Local Regularity, Infinite Products of Matrices and
Fractals" (SIAM J. Math. Anal., 22(5):1388-1410 and 23(4):1031-79, respective-
ly). Those papers discuss the solution of two-scale difference equations
f(x) = sum_{n=0}^{N} c_n f(kx - n)
(which, for k = 2, is of course the fundamental equation governing multireso-
lution analysis scaling functions). If a solution f exists and is l-times
differentiable, simple differentiation of the above equation shows that
f^(l) (x) = sum_{n=0}^{N} k^l c_n f^(l) (kx - n),
i.e., f^(l) satisfies a two-scale difference equation with coefficients k^l c_n
rather than simply c_n. So any method which computes the scaling function phi
from the dilation coefficients c_n can be used to compute phi^(l), assuming
that phi is l-times differentiable and that the method converges; simply use
2^l c_n in place of c_n. And since the wavelet psi can be computed from phi,
specifically, psi(x) = sum_{n=0}^{N} (-1)^n c_{1-n} phi(2x - n), psi is l-times
differentiable whenever phi is, and we have
psi^(l) (x) = sum_{n=0}^{N} 2^l (-1)^n c_{1-n} phi^(l) (2x - n).
In particular, the papers discuss how to compute solutions to two-scale
difference equations exactly on the dyadic rationals (i.e., x = 2^{-j} m,
j and m integers; we are considering the multiresolution case with k = 2).
The method comes from the observation that if we know the exact values of phi
on the integers, then the difference equations allow us to compute exactly its
values on the half-integers, and from those the exact values on the quarter-
integers, and so on, and that the exact values of phi on the integers can be
found by solving for the eigenvector with eigenvalue 1 of a particular matrix
(and normalizing appropriately). This observation holds essentially true when
solving for a derivative of phi, except that the values of phi^(l) on the
integers correspond to the eigenvector with eigenvalue 2^{-l}. The eigenvector
normalization is straightforward when l = 0 (i.e., when solving for phi) but
a little involved when l >= 1. For details, see the papers themselves or send
me email.
Good luck,
Mitch Oslick
mho@nova.stanford.edu
--------------------------- Topic #13 -----------------------------------
From: a.bharath@ic.ac.uk
Subject: Answer: Frequency Modulation Laws (WD 4.4 #15)
In reply to the question from Paulo Seleghim Junior, in Wavelet Digest
Volume 4, no. 4, (Topic 15) on Frequency Modulation Laws, I submit the
following:
The paper by Delprat, Escudie at al, entitled "Asymptotic Wavelet and Gabor
Analysis: Extraction of Instantaneous Frequencies" (IEEE Transactions on
Information Theory), vol 38, no 2, 1992, pp644-664) gives a comprehensive
review and application examples of wavelet scale-space ridges for the
extraction of frequency modulation laws from *asymtotic signals*. You
will find that the stationary phase approximation is appropriate for this
class of signals.
For more information on the stationary phase approximation itself, consult
the text by E. Copson, called Asymptotic Expansions, Chapter 4: "The Method of
Stationary Phase", Cambridge Univ. Press, 1965, pp27-35.
I can also provide a reprint of some work that I did on the subject, published
within the Univ. of London.
Dr. A. A. Bharath
Hayward Lecturer in Medical Imaging
Centre for Biological & Medical Systems
Imperial College, London
Tel: 44-(0)171-594-5183
E-Mail: a.bharath@ic.ac.uk
--------------------------- Topic #14 -----------------------------------
From: andrewd@ee.uts.edu.au (Andrew Dorrell)
Subject: Answer: Reference missing in Daubechies' Ten lectures ?
The following is a response to my question which I have not seen posted to
the list yet (although you may have received it since the last posting).
Question: Reference missing in Daubechies' Ten lectures ?
Answer:
From: "S.PITTNER Diss.Wavelets" <pittner@uranus.tuwien.ac.at>
Subject: Response concerning Daubechies reference
I only know two articles that fit to your question. They are
both contained in my bibliography and are listed below
supplemented by abstracts. I think that Ingrid Daubechies
had the first one in mind.
Stefan Pittner
M. Antonini, M. Barlaud, P. Mathieu,
Predictive Interscale Image Coding Using Vector Quantization,
in ``Signal Processing V: Theories and Applications''
(L. Torres, E. Masgrau, M. A. Lagunas, Eds.), Vol. 2, Elsevier Science
Publishers, Amsterdam, 1990, pp. 1091--1094.
The authors propose a new method for image compression
associating the biorthogonal wavelet transform and an interscale
prediction scheme. They use a biorthogonal wavelet transform in order
to obtain a set of images at different scales and for different
orientations. The method consists of predicting the position and the
amplitude of the edges at a given scale using the edges of the lower
scales. They also propose an interscale vector quantization scheme
which accounts for the correlation between the wavelet coefficients
inside the classification algorithm (LBG or KOHONEN neural network
algorithms).
M. Antonini, M. Barlaud, P. Mathieu, I. Daubechies,
Image Coding Using Vector Quantization in the Wavelet Transform Domain,
Proc. of the IEEE Int. Conf. on Acoust., Speech and Signal Processing, Vol. 4,
Albuquerque, 1990, pp. 2297--2300.
Image compression is now essential for applications such as transmissions
and storage in databases. This paper proposes a new scheme for image
compression that takes into account psychovisual features both in the space and
frequency domains; this new method involves two steps. First, the authors use
a wavelet transform in order to obtain a set of orthonormal subclasses of
images; the original image is decomposed at different scales using a
pyramidal algorithm architecture. The decomposition is along the vertical
and horizontal directions and maintains constant the number of pixels
required to describe the image. Second, according to Shannon\'\/s rate
distortion theory, the wavelet coefficients are vector quantized using a
multiresolution codebook. Furthermore, to encode the wavelet coefficients
the authors propose a noise shaping bit allocation procedure which assumes
that details at high resolution are less visible to the human eyes. Finally,
in order to allow the receiver to recognize a picture as quickly as possible
at minimum cost they present a progressive transmission scheme. In fact, it
is shown that the wavelet transform is particularly well-adapted to the
progressive transmission.
--------------------------- Topic #15 -----------------------------------
From: "Ole Moller Nielsen" <uniomni@uni-c.dk>
Subject: Question: How to obtain Paper on Connection Coefficients.
Many papers refer to
Aware Technical Report AD910708, 1991
"The Evaluation of Connection Coefficients of Compactly Support Wavelets"
by A. Latto, H. L. Resnikoff and E. Tenenbaum.
I have so far been unable to locate this.
If anybody knows how to obtain a copy, I would be grateful for that
information.
Thank you in advance
Ole Moller Nielsen
Email: uniomni@uni-c.dk
--------------------------- Topic #16 -----------------------------------
From: PSOMMA@chiostro.univr.it
Subject: Question: Application of wavelets to fractal signals.
We are interested with applications of wavelets to fractal
signals.
If someone knows preprints, papers, books on this subject, please
send the reference to
psomma@chiostro.univr.it
in particular we are looking for
A. Arneado, E. Bacry, AND J. F. Muzy `Wavelet analysis of fractal
signals', preprint, September 1991
Thanks,
Paolo Sommaruga Stefano Lonardi
Universita' di Verona Universita' di Padova
Italy Italy
--------------------------- Topic #17 -----------------------------------
From: Daniel Coca <coca@acse.shef.ac.uk>
Subject: Question: Truncated sequences for B-spline wavelet.
Hello there!
I wonder if there is anyone who can tell me if the (truncated)
decomposition sequences for the B-spline wavelet and scaling functions
of order greater than 4 are available somewhere. I have the formula to
calculate them but it seems a bit complicated to apply it in this
case.
Many thanks
Daniel
--------------------------- Topic #18 -----------------------------------
From: rannou@cs.utk.edu
Subject: Question: Looking for code with non power of 2 length signals
Hello,
I'm looking for C code (or matlab) to compute the wavelet decomposition
to an array of length other than a power of 2. Also, I need the algorithm
to construct the matrix W representing the same transformation as above.
Thanks a lot
Fernando Rannou
--------------------------- Topic #19 -----------------------------------
From: vidyut!motwa@vigyan.iisc.ernet.in
Subject: Question: Triadic Haar wavelets problem
1st April '95
IISc.,Bangalore
Dear Waveletters,
We are working with a problem involving triadic wavelets where we have
the MRA given by
f(x) belogs to Vj implies and is implied by f(3x) belongs to Vj+1
But for the Haar basis we are not able to get the wavelet which will generate
the basis for the space.
Kindly mail at motwa@vidyut.ee.iisc.ernet.in if you have any answer.
Bye
Motwani
--------------------------- Topic #20 -----------------------------------
From: Frederic Gilbert <Frederic.Gilbert@inria.fr>
Subject: Internet: A newly released WWW server : INRIA Fractales Project.
The Fractales Project from the INRIA French research institute is
pleased to inform you that it has given public access to its
Mosaic server. This server encloses summaries, demonstrations and
software packages related to most of the Fractales Project
studies, oriented toward applications of fractal theory to 1D and
2D signals analysis.
You can access it by the following Uniform Resource Locator :
http://www-rocq.inria.fr/fractales/
Feel free to connect and to send us your comments.
-------------------- End of Wavelet Digest -----------------------------