Wavelet Digest, Vol. 07, Nr. 04.
Ken Jackson
Wavelet Digest Friday, April 17, 1998 Volume 7 : Issue 4
Today's Editor: Wim Sweldens
Lucent Technologies, Bell Laboratories
w...@bell-labs.com
Your e-mail address: k...@cs.toronto.edu
Today's Topics:
1. Book: Applications of Wavelets: Case Studies
2. Preprint: Empirical Tests for Multi-rate Filter Banks
3. Preprint: Projections of ICT denoising based on wavelet maxima
4. Preprint: Discrete Wavelet Transform on Digital Signal Processors
5. Thesis: Factoring Wavelet Transforms
6. Thesis: Matrix compression in wave scattering
7. Course: Wavelets and Filter Banks (Strang-Nguyen)
8. Course: Multimedia courses on wavelet based image processing
9. Meeting: Advanced Modeling In Applied Computational Electromagnetics
10. Job: Postdoctoral Position in France
11. Contents: Numerical Algorithms 16-3,4
12. Contents: "Computerra" special issue on wavelets
13. Contents: J. Approx. Th. - mar98 TOC
14. Answer: Papers on Discrete Wavelet Multi-Tone (DWMT) (WD 7.3 #23)
15. Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)
16. Question: Mathematics of Wavelets
17. Question: Wavelet Transformation in medical diagnosis
18. Question: Wavelets and fractal data characterization.
19. Question: Wavelets for multi-dimensional density estimation
20. Question: Wavelets and pattern classification.
21. Question: Wavelets and dense linear systems.
22. Question: Multiple Time Series Analysis by Wavelet Approach
23. Question: Ridge and skeleton extraction
24. Question: Morlet wavelet
25. Question: Wavelets & super-resolution of 2d images?
26. Question: Error in Matlab wavelet toolbox manual?
27. Question: Ordering of Wavelet packets in Matlab wavelet toolbox?
28. Question: Gaussian Wavelets
Current number of members: 11427
E-mail:
General help: he...@wavelet.org
Add yourself as a member: a...@wavelet.org
Remove yourself as a member: rem...@wavelet.org
Publish in the next WD: pub...@wavelet.org
Receive publishing policy: pol...@wavelet.org
Visit us on the Web at http://www.wavelet.org/
Calendar of events:
*May 20-22: Wavelets and Filter Banks (Strang-Nguyen), Boston WD 7.4 #7
Jun 1-12: Multiscale approaches for PDE, Marseilles, France WD 7.3 #9
Jun 8-12: Wavelets, Neural Networks, Fuzzy Logic, Chaos, UCLA WD 7.3 #10
Jun 22: IEEE Multimedia compression, Santa Barbara, CA WD 6.10 #12
Jun 29-Jul 10: EMS Summer School on Wavelets, Paris WD 7.2 #9
Jul 8-10: Nonlinear Modeling, Leuven, Belgium WD 7.2 #8
Jul 30-Aug 7: Workshop on Self-Similar Systems, Dubna, Russia WD 6.12 #10
*Sep 28-30: Applied Computational Electromagnetics, Penn State WD 7.4 #9
Oct 4-9: School on Wavelets in the geosciences, Delft, Netherl. WD 7.1 #12
Oct 5-8: 10th GAMM-Workshop on Multigrid Methods, Bonn, Germany WD 6.12 #11
----------------------------------------------------------------------
Date: Wed, 25 Mar 98 12:40:46 -0500
From: leb...@siam.org
Subject: #1 Book: Applications of Wavelets: Case Studies
Applications of Wavelets
Case Studies
Edited by Mei Kobayashi
Available September 1998
Approx. 175 pages / Softcover / ISBN 0-89871-416-8
List Price $32.00 / SIAM Member Price $25.60 / Order Code OT62
This collection of independent case studies demonstrates how
wavelet techniques have been used to solve open problems and
develop insight into the nature of the systems under study. Each
case begins with a description of the problem and points to the
specific properties of wavelets and techniques used for
determining a solution.
The cases vary from a very simple wavelet-based technique to
reduce noise in data to work conducted at the Earthquake Research
Institute in Japan. One case study shows how wavelet analysis is
used in the development of a Japanese text-to-speech system for
personal computers and another presents new wavelet techniques
developed for and applied to the study of atmospheric wind,
turbulent fluid, and seismic acceleration data.
Although calculus and some junior and senior mathematics courses
for scientists and engineers will suffice, a solid background in
undergraduate mathematics, particularly analysis and numerical
analysis, and some familiarity with the basics of wavelets are
helpful for reading this book.
Contents (partial) Preface; Chapter 1: Multiresolution Display of
Coastline Data, Sumiko Hiyama and Mei Kobayashi; Introduction;
Properties of Scaling Functions and Wavelets; Approximation of
Curves Using Mallat's Algorithm; Conclusion; Chapter 2: A
Technique for Reducing Noise in Laboratory Data, Susumu
Sakakibara; Introduction; Wavelets and a Data Smoothing Method;
Two Examples; Conclusion; Chapter 3: A Conjugate Gradient Method
for Solving Poisson Equations, Nobuatsu Tanaka; Introduction; The
Incomplete Discrete Wavelet Transform; Numerical Examples;
Conclusion; Chapter 4: Wavelet Analysis for a Text-to-Speech
System, Mei Kobayashi, Masaharu Sakamoto, Takashi Saito, Yasuhide
Hashimoto, Masafumi Nishimura, Kazuhiro Suzuki; Introduction;
Wavelets and Speech Signal Processing; Text-to-speech Conversion;
Conclusion; Chapter 5: Analysis of Atmospheric Wind, Turbulent
Fluid, and Seismic Acceleration Data, Michio Yamada and Fumio
Sasaki; Introduction; Extraction of Events from Time-Series;
Spatial Distribution of Fourier Components; Correction of Seismic
Data; References.
About the Author Mei Kobayashi is a researcher at IBM Tokyo
Research Laboratory and a visiting associate professor in the
Department of Mathematical Sciences at the University of
Tokyo. She is a frequent contributor to SIAM News.
------------------------------
Date: Tue, 24 Mar 1998 15:43:16 -0800
From: Carl Taswell <tas...@toolsmiths.com>
Subject: #2 Preprint: Empirical Tests for Multi-rate Filter Banks
Title: Empirical Tests for the Evaluation of Multi-rate Filter Bank Parameters
Author: Carl Taswell
Submitted: March 1998 to IEEE TCAS-II
Available: www.toolsmiths.com/fwmrfbp.shtml with complete set of
multi-color figures to accompany the preprint (example demonstrated in
figures is 4-band 2-regular orthogonal wavelet filter bank).
Empirical tests are developed for evaluating and characterizing
multi-rate $M$-band filter banks represented as $N\times M$ matrices
of filter coefficients. Each test returns a numerically observed
estimate of a $1\times M$ row vector of parameters with each parameter
element corresponding to a filter band column vector of the filter
bank matrix. These vector valued parameters can be readily converted
to scalar valued parameters for comparison of given filter banks or
optimization in filter bank design. Tests are defined and demonstrated
for $M$-band reconstruction error and delay, $M$-shift biorthogonality
and orthogonality errors, frequency domain selectivity, time frequency
uncertainty, time domain regularity and moments, and vanishing moment
numbers. These tests constitute the verification component of the
first stage of the hierarchical three stage framework (with filter
bank coefficients, single-level convolutions, and multi-level
transforms) for specification and verification of the reproducibility
of wavelet transform algorithms. Example filter banks tested include
a variety of real and complex orthogonal, biorthogonal, and
nonorthogonal $M$-band systems with $M\geq 2$. Coefficients for these
filter banks were either generated by computational algorithms or
obtained from published tables. The examples demonstrate the
importance of the methodology in revealing discrepancies between
observed and expected results, and thus, in insuring scientific
reproducibility of results and conclusions.
------------------------------
Date: Fri, 27 Mar 1998 16:04:55 +0800
From: app...@cqu.edu.cn
Subject: #3 Preprint: Projections of ICT denoising based on wavelet maxima
Abstract
Industrial Computerized Tomography (ICT) is
different from medical computerized tomography. The density of
industrial components are high, and the construction of industrial
components are complex. In ICT, we scan the industrial component with
rays from different directions. From projections, we reconstruct the
image of a cross section of the industrial component. ICT be use for
non-damage detection of industrial components. ICT can be applied on
space and aeronautical engineering, machine building, oil detection
,et..
Because the effect of physics factors, there is
noise in projections .After reconstruction of image, the noise will be
enhanced. And, the white noise in projections can be transformed into
non-white noise in reconstructed image. How to reduce the noise in a
image of ICT and not damage the edge of the image, is a difficult
question of image process. Wavelet transform maxima can describe the
different singularities of the edge signal and the noise . So, wavelet
transform maxima can filter the noise and keep the edge signal
. Firstly, we filter projections by wavelet transform maxima.
Secondly, we reconstruct image of ICT. These method can reduce the
noise in the image of ICT and can filter the non-white noise.
------------------------------
Date: Wed, 08 Apr 1998 19:36:00 +0100
From: Thomas Sinnwell <t.sin...@rz.uni-sb.de>
Subject: #4 Preprint: Discrete Wavelet Transform on Digital Signal Processors
Authors: Thomas Sinnwell, Stefan Sinnwell, K.-D. Becker
Universitaet des Saarlandes
Theoretische Elektrotechnik
Germany
Title: Efficient Implementation of the Discrete Wavelet Transform on
Digital Signal Processors
e-mail: t.sin...@rz.uni-sb.de
Abstract:
The wavelet transform (WT) is a very powerful tool for the analysis of
transient signals. An efficient implementation of the discrete form of
the wavelet transform on digital signal processors (DSPs) is
especially interesting for the analysis of real time signals. The
present paper begins by presenting and discussing the continuous
wavelet transform. The transition to the discrete WT is then explained
and executed. After a short discussion of the possibilities of
implementing the discrete WT, the implementation of the periodic
extension of the discrete WT on digital signal processors is
described. Within this context, special attention is given to circular
addressing as a special form of indirect addressing. The corresponding
assembly code is described for the digital signal processor TMS320C3X
series from Texas Instruments.
Keywords: Wavelet transform (WT), Multiresolution analysis (MRA), Digital
signal processors (DSPs)
Status: Submitted to Applied Signal Processing
The preprint is available as PDF file at
http://tews2.ee.uni-sb.de/preprints.html
------------------------------
Date: Wed, 18 Mar 1998 16:40:29 +0800
From: Paul Abbott <pa...@physics.uwa.edu.au>
Subject: #5 Thesis: Factoring Wavelet Transforms
Factoring Wavelet Transforms
Mark Maslen <m...@physics.uwa.edu.au>
The discrete wavelet transform can be carried out using a sequence of
simple operations called lifting steps. The theory of lifting may be
developed by considering the polyphase representations of the filters
for a given basis, defined in terms of Laurent polynomials. The
polyphase matrix is constructed from these polynomials, and this
matrix is used to carry out the wavelet transform. Using the Euclidean
algorithm for Laurent polynomials, the polyphase matrix may be
factorised, giving rise to the sequence of lifting steps. An important
algebraic result is that the quotients determined from this algorithm
are not uniquely defined, so there are several possible
factorisations. This allows a choice of optimal factorisation for a
given purpose. In this project, a program was developed to find all
factorisations of a given filter. The inverse of the wavelet
transform, when expressed in terms of lifting steps is simple to find,
and this too has been automated. It is demonstrated that for large
datasets, the lifting implementation is significantly faster than the
traditional method of conducting the wavelet transform via quadrature
mirror filters.
http://www.pd.uwa.edu.au/~paul/publications.html
------------------------------
Date: Wed, 25 Mar 1998 11:32:21 +0000
From: Zachi Baharav <za...@hp.technion.ac.il>
Subject: #6 Thesis: Matrix compression in wave scattering
Thesis Title: "Basis construction for efficient scattering analysis"
Author: Zachi Baharav
Supervisor: Prof. Y. Leviatan
Abstract
This work deals with the numerical solution of electromagnetic
scattering problems. The motivation for the work is the wish to reduce
the problem complexity when dealing with scattering by bodies
containing wide range of length-scales. The work deals mainly with the
integral formulation of the problem, followed by a Method of Moments
discretization process. A few methods to reduce the size of the
resulting impedance matrix, and thus ease the computational burden are
presented. The common feature of all these methods is that instead of
trying to render the impedance matrix sparse (as previous methods do),
these methods strive at a smaller impedance matrix. Thus, instead of
solving a (possibly sparse) large matrix, we face a much smaller
matrix. Moreover, these methods have applications to solution
refinement procedures, finite-array structures, and more. The main
theme of all these methods is to combine ideas from the
signal-processing community (wavelets, filters, compression, alike),
with the insight into the physics of the problem (physical optics,
radiation patterns, and alike), to facilitate an easier solution
process.
The thesis is available at
http://shaked.technion.ac.il/~zachi
Zachi Baharav
e-Mail: za...@hp.technion.ac.il
------------------------------
Date: Fri, 3 Apr 1998 13:57:58 -0500 (EST)
From: Gil Strang <g...@math.mit.edu>
Subject: #7 Course: Wavelets and Filter Banks (Strang-Nguyen)
WORKSHOP COURSE ON WAVELETS AND FILTER BANKS
taught by Gilbert Strang (MIT) and Truong Nguyen (Boston University)
Wednesday-Thursday-Friday **May 20-21-22, 1998**
at Wellesley College ( a beautiful campus outside Boston )
TEXT: Participants will receive the new textbook (revised edition in 1997)
WAVELETS AND FILTER BANKS by Strang and Nguyen
Wellesley-Cambridge Press, Box 812060, Wellesley MA 02181
This text is already in class use in many EE and mathematics departments.
It was chosen to accompany MATLAB's Wavelet Toolbox, which will be the
simulation software at the Wavelet Workshop. It can be ordered by email.
We also have a new IMAGE CODER by Truong Nguyen (1997)
This will be used at the Workshop and will be provided to participants.
We will aim for the right balance of theory and applications. The text
gives an overall perspective of the field - which continues to grow
with amazing speed. The topics will include
1. Analysis of Filter Banks and Wavelets
2. Design Methods
**3. Applications (from Lecturers and Participants)
4. Hands-on Experience with Software (including image coding)
These four key areas will be developed in detail:
1. Analysis
Multirate Signal Processing: Filtering, Decimation, Polyphase
Perfect Reconstruction and Aliasing Removal
Matrix Analysis: Toeplitz Matrices and Fast Algorithms
Wavelet Transform: Pyramid and Cascade Algorithms
Daubechies Wavelets, Orthogonal and Biorthogonal Wavelets
Smoothness, Approximation, Boundary Filters and Wavelets
Time-Frequency and Time-Scale Analysis
2. Design Methods
Spectral Factorization
Cosine-Modulated Filter Banks
Eigenfilters and Quadratic Constrained Least Squares
Lattice Structure
The Lifting Method (Ladder Structure)
3. Applications
Audio and Image Compression, Quantization Effects
Transient Detection and Edge Detection
Digital Communication and Multicarrier Modulation
Transmultiplexers
Text-Image Compression: Lossy and Lossless
Medical Imaging and Scientific Visualization
Image Compression / Image Segmentation / Image Enhancement
Video Compression
4. Simulation Software
MATLAB Wavelet Toolbox
ECG Compression
New IMAGE CODER
The goal of the Workshop is to be as useful as possible to all
participants. ** Please request information by an email message
with subject Workshop to the organizer
Gilbert Strang: g...@math.mit.edu
We will reply about the program and tuition cost and housing.
The tuition includes the textbook and software. It will be the same as
in 1995, 1996, and 1997 (San Jose, Tampa, San Diego, and Fairfax Workshops).
It is reduced by 50% for graduate students. We are very glad to
answer all questions by email. Our Web sites are
http://saigon.ece.wisc.edu/~waveweb/QMF.html http://www-math.mit.edu/~gs
Gilbert Strang Room 2-240 MIT Cambridge MA 02139
617 253 4383 fax 617 253 4358 g...@math.mit.edu
------------------------------
Date: Thu, 19 Mar 1998 16:51:37 +0200
From: "PHILIP" <phis...@med.upatras.gr>
Subject: #8 Course: Multimedia courses on wavelet based image processing
The PRONET system, which is the product of the "PRONET - Multimedia Computer
Based On-Line Training and Support Service for Professionals" project (DG
XIII - ET 1017) is an integrated telematics network service for the training
and support of researchers and professional specialists. PRONET supports the
following functions: on-line multimedia computer based training courses with
tutoring support system,information database services,communication services
between professionals.
A part of the "Biomedical Signal & Image Processing" course, deals with
wavelet theory and some applications on medical image processing:
compression, denoising, contrast enhancement. The emphasis is given on the
multimedia character of the course: the texts are small and they are
supported by a large number of original graphs, images, animations and
sound.
To take the courses visit http://pronet.eurocom.gr and register as a new
user (registration up to now is free :).
At "category of your interest" choose "Biomedical engineers and medical
physicists". Then choose "Training services", " Biomedical Engineering",
"Biomedical Signal & Image Processing ", register to course and finally
download the stand-alone course zip files.
Send your comments or questions (for the wavelet lessons) at
phis...@med.upatras.gr
------------------------------
Date: 20 Mar 1998 14:56:35 -0500
From: "posting" <pos...@omnibus.ce.psu.edu>
Subject: #9 Meeting: Advanced Modeling In Applied Computational Electromagnetics
ADVANCED MODELING IN APPLIED COMPUTATIONAL ELECTROMAGNETICS
SEPTEMBER 28-30, 1998
The Penn Stater Conference Center Hotel
State College, Pennsylvania
The Penn Stater Conference Center Hotel and the Applied Computational
Electromagnetics Society (ACES) have joined forces to provide you with
a unique opportunity - three days of short courses and hands-on
workshops which treat modeling in the frequency domain (Method of
Moments - MOM), time domain (Finite Difference Time Domain - FDTD,
Transmission Line Modeling - TLM), applications of MATHCAD and MATLAB
in the frequency and time domains, representation of fields and
geometries for modeling, wavelets, and modeling of propagation and
interference in communication systems. Also being covered will be
ray-tracing techniques for mobile communications, fast solvers for
Maxwell's integral equations, model-based parameter estimation, and
genetic algorithms.
For complete details and up-to-date information, please visit the web site at:
http://www.outreach.psu.edu/C&I/ACES/
FOR MORE INFORMATION
About program content:
Richard W. Adler
833 Dyer Road/ RM 437/ Code ECAB
Naval Postgraduate School
Monterey CA 93943-5121
Phone: (408) 656-2352
Fax: (408) 649-0300
E-mail: r...@ibm.net
About registration:
Lori Benson, Conference Planner
The Pennsylvania State University
225 The Penn Stater Conference Center Hotel
University Park PA 16802-7002
Phone: (814) 863-5120
E-mail: Confere...@cde.psu.edu
a continuing and distance education service of the College of
Engineering in cooperation with the Applied Computational
Electromagnetics Society
To receive a brochure with registration materials, nationwide, call
1-800-PSU-TODAY (1-800-778-8632) or send us an e-mail with your name,
address, phone number, fax number, and Internet address to
Confere...@cde.psu.edu . Please be sure to reference ADVANCED
MODELING IN APPLIED COMPUTATIONAL ELECTROMAGNETICS in all
correspondence.
For information about all of Penn State's upcoming programs, visit our Web
site: http://www.outreach.psu.edu
------------------------------
Date: 23 Mar 1998 13:10:02 +0000
From: van.bu...@ifp.fr
Subject: #10 Job: Postdoctoral Position in France
POST DOCTORAL POSITION Available at Institut Francais du Petrole
- FRANCE-
Post Doctoral Position is available immediately to develop
wavelet based techniques for Computer Graphics (interactive
simplifications of Surfaces, 2D and 3D Meshes based on their
wavelet representations).Experience in wavelet, multiresolution
signal processing is necessary. Candidates with background on
Computer Graphics, Image Processing will be preferred.
Send Curriculem-Vitae to:
Dr Van Bui-Tran
Image & Signal Processing Group
Department of Computer Science and Applied Mathematics
Institut Francais du Petrole
1 & 4 av de Bois-Preau
92500 Rueil-Malmaison
FRANCE
email: van.bu...@ifp.fr
fax: +FRANCE 1 47 52 70 22
------------------------------
Date: Thu, 19 Mar 1998 10:09:41 +0100
From: Baltzer Science <mai...@ns.baltzer.nl>
Subject: #11 Contents: Numerical Algorithms 16-3,4
Numerical Algorithms 16 (1997) 3,4
Kai Diethelm and Guido Walz
Numerical solution of fractional order differential equations by
extrapolation 231-253
Rosemary Renaut and Yi Su
Evaluation of Chebyshev pseudospectral methods for third order differential
equations 255-281
Milvia Rossini
Irregularity detection from noisy data in one and two dimensions 283-301
Sven Ehrich
Sard-optimal prefilters for the Fast Wavelet Transform 303-319
P. Verlinden, D.M. Potts and J.N. Lyness
Error expansions for multidimensional trapezoidal rules with Sidi
transformations 321-347
W.H. Enright and H. Hayashi
A delay differential equation solver based on a continuous Runge--Kutta
method with defect control 349-364
Xiu Ye and Charles A. Hall
A discrete divergence-free basis for finite element methods 365-380
Claude Brezinski
Book reviews 381-382
------------------------------
Date: 23 Mar 1998 10:06:10 +0000
From: "Leonid I. Levkovich" <lev...@spp.keldysh.ru>
Subject: #12 Contents: "Computerra" special issue on wavelets
This is to announce the special issue of the popular Russian
computer-oriented weekly magazine "Computerra"
(http://www.cterra.com), devoted to wavelets: Computerra, #8(236), 2,
March, 1998. Here's the list of papers (all of them in Russian).
G.Bashilov, L.Levkovich-Maslyuk
Smallish-wave analysis
V.Spiridonov
The splash of revolutions
L.Levkovich-Maslyuk
The digest of wavelet analysis, in 2 formulas and 22 pictures
P.Frick, D.Sokolov
Wavelets in astrophysics and geophysics
Yu. Farkov
Mathematics of wavelets in Russia (a brief review)
V.Spiridonov
Self-similarity, wavelets and quasicrystalls
T. Lambrou, A. Linney, R. Speller
WAVELET TRANSFORM APPLICATIONS IN MEDICAL SIGNALS AND IMAGES
A.Pereberin
Wavelets in computer graphics
The next issue contains another wavelet-oriented paper, originally prepared for the special issue:
Computerra, #9(237), 9, March, 1998.
Graham Seaman
Wavelets in programmable silicon
------------------------------
Date: Tue, 24 Mar 1998 09:50:40 -0500 (EST)
From: Thomas Hogan <ho...@math.ohio-state.edu>
Subject: #13 Contents: J. Approx. Th. - mar98 TOC
Table of Contents: J. Approx. Theory, Volume 92, Number 3, March 1998
Shu-Sheng Xu
On characterization of best approximation with certain constraints
339--360
S. Clement Cooper and Philip E. Gustafson
The strong Chebyshev distribution and orthogonal Laurent polynomials
361--378
Michael I. Ganzburg
Best approximation of functions like $|x|^\lambda\exp(-A|x|^{-\alpha})$
379--410
J. M. Carnicer, J. M. Pe\~na, and R. A. Zalik
Strictly totally positive systems
411--441
Boris P. Osilenker
Trace formula for orthogonal polynomials with asymptotically 2-periodic
recurrence coefficients
442--462
Ying Guang Shi
A minimax problem admitting the equioscillation characterization of
Bernstein and Erd\H{o}s
463--471
David Ruch and Jianzhong Wang
Connections between the support and linear independence of refinable
distributions
472--485
Ulrich Schmid
On the approximation of positive functions by power series, II
486--501
Author index for Volume 92
502
------------------------------
Date: Wed, 18 Mar 1998 10:07:01 EST
From: p-sc...@epo.e-mail.com
Subject: #14 Answer: Papers on Discrete Wavelet Multi-Tone (DWMT) (WD 7.3 #23)
Dr. Tressler asked for publications on discrete wavelet multitone
transmission. Here are three references.
Discrete wavelet multitone (DWMT) system for digital
transmission over HFC links
Gross; Tzannes; Sandberg; Padir; Zhang
Proceedings of the SPIE 1995
VOL 2609
pages 168-175
Overlapped discrete multitone modulation for high speed copper wire
communications
Sandberg; Tzannes
IEEE Journal on Selected Areas Communications, Dec. 1995
VOL 13, No 9.
pages 1571-1585
DMT systems, DWMT systems and digital filter banks
Tzannes; Tzannes; Proakis; Heller
ICC 1994 1-5 May 1994
page 311-315
Paul Scriven
------------------------------
Date: Tue, 24 Mar 1998 11:05:27 -0800
From: Kevin Bowman <kevin....@jpl.nasa.gov>
Subject: #15 Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)
Dear Andrew,
I recently came across some responses to your enquiry. I have
extended Beylkin's technique into 2-D for a variety of different kinds
of wavelets. Basically, I convert the integral operator into a 4-D
wavelet basis in non-standard form. I describe this technique in part
in "Application of wavelets to wavefront reconstruction in adaptive
optical systems" SPIE vol 3126 "Adaptive Optics and Applications" pp
288-299. For a full description you can get my Phd thesis
"Application of Wavelets to Adaptive Optics and Multiresolution Wiener
Filtering" from Georgia Institute of Technology, 1997. I think you
can obtain my dissertation from UMI at http://www.umi.com
Regards,
Kevin Bowman
Kevin W. Bowman, PhD.
Jet Propulsion Laboratory
4800 Oak Grove Drive, MS 169-315
Pasadena, CA 91109
------------------------------
Date: Wed, 18 Mar 98 19:31:18 GMT
From: Thomas Harte <thomas...@cl.cam.ac.uk>
Subject: #16 Question: Mathematics of Wavelets
Hallo,
I have an electronic engineering background and I am interested in
reading the mathematics relevant to wavelets in some depth. Many
wavelet texts have reasonable introductions to functional analysis,
measure theory, Lebesgue integration, function spaces, and so on, but
most are limited (naturally) to presenting but the most cursory of
outlines.
For example, [L. Prasad & S.S Iyengar (1997) ``Wavelet Analysis with
Applications to Image Processing'', CRC Press, Boca Raton] goes some
way towards unravelling the mysteries of wavelet maths, but it has
only ~200pages and many topics are covered at the level one would
expect in a short discourse.
[Q.] What texts have YOU found to be most helpful on the topics of
functional analysis, measure theory, Lebesgue integration, &c. given
that your background is engineering/physical sciences, and *not*
mathematics? [Please note I am *not* looking for yet another
introduction-to-wavelets text.]
I would appreciate any bibliographies which you may have compiled.
Many thanks,
Thomas Harte.
------------------------------
Date: Mon, 23 Mar 1998 17:03:49 +0800
From: Tang Yipeng <ta...@kalsoft.online.sh.cn>
Subject: #17 Question: Wavelet Transformation in medical diagnosis
I wondering if you could provide me some samples of Wavelet application
in medical diagnosis.
------------------------------
Date: Mon, 23 Mar 1998 01:25:24 PST
From: "Naren Mohan" <m_n...@hotmail.com>
Subject: #18 Question: Wavelets and fractal data characterization.
Dear Waveleteers,
I am an undergraduate Student of Electrical and Electronics and am
working on a project which involves analysis of fractal data using
wavelets. I have taken Fractional Brownian motion as my model and i
have simulated it using computer. Now i need to confirm whether it is a
fractal data. If yes, then in what way should we adjust the scaling of
the wavelet so as to estimate the dimension of the signal.
Thanks in advance
Yours Sincerely,
Mohan Naren
m_n...@hotmail.com
------------------------------
Date: Mon, 23 Mar 1998 16:14:09 +0000 (GMT)
From: "Rui. Shao" <rui....@newcastle.ac.uk>
Subject: #19 Question: Wavelets for multi-dimensional density estimation
Dear Waveletters,
I am a postgrad in the Department of Chemical and Process Engineering,
university of Newcastle, UK. My research interest is the application
of wavelet transform in chemical process monitoring, etc.
Density estimation using wavelets is a very interesting topic for me
and I have obtained satisfactory results in one-dimensional
case. Daubechies' wavelets are adopted; the square-root of the density
function is estimated first according to Pinheiro and Vidakovic
(1995); wavelet thresholding proposed by Donoho, etc. is also used.
However I find the multi-dimensional density estimation extremely
difficult. The main problems include: curse of dimensionality, number
of wavelets required growing exponentially with the dimension,
computation complexity... I tend to use Wave-Net to solve this but not
sucessful. I wonder is there anyone has given any practical solution
to this problem?
Any help or hints would be highly appreciated!
yours hopefully,
Rui Shao
------------------------------
Date: Tue, 24 Mar 1998 13:15:11 -0700
From: Arun <arun....@ualberta.ca>
Subject: #20 Question: Wavelets and pattern classification.
Hi
Can anyone tell me of a 'simple' work on pattern classification using
wavelets. Not too mathematical but a simple illustration ?.
Thank you
--
-Arun
Arun....@UAlberta.ca : http://www.ualberta.ca/~akt1
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Date: Fri, 27 Mar 1998 10:40:40 +0100
From: Patricia Gonzalez Gomez <patr...@dec.usc.es>
Subject: #21 Question: Wavelets and dense linear systems.
Dear Waveletters,
I'm looking for information about wavelets and numerical analysis. I
am interested in solving dense linear systems and I am trying wavelet
transforms to make them sparse. I know the work of Beylkin, Coifman
and Rokhlin and that of Bond and Vavasis, I would appreciate if you
could point me any other reference on this subject.
Moreover, I would like to use wavelets to solve linear systems arising
from coupled BEM/FEM codes, where part of the coefficient matrix is
dense and the other part is sparse. Does anybody have information
about this subject?
Thanks in advance,
Patricia
Patricia Gonzalez Gomez
Dpt. Electronics and Computer Science. Fac. Fisica
Univ. Santiago de Compostela. E-15706. (SPAIN)
Phone: +34 81 563100 Ext. 13564 Fax: +34 81 599412
E-mail: patr...@dec.usc.es
------------------------------
Date: Mon, 30 Mar 1998 16:20:06 +0400
From:wim Tue Mar 31 10:34:24 EST 1998 remote from shovel
Subject: #22 Question: Multiple Time Series Analysis by Wavelet Approach
Dear WaveletDiggest !
I am working in area of processing multidimensional time series, which
were obtained from geophysical monitoring systems. One purpose of my
analysis is searching precursors of strong earthquakes as an
increasing of collective behaviour of variations of different
geophysical fields. I have some experience of using such classical
tools of multidimensional time series analysis as spectral matrices
maximal eigenvalues and canonical coherences. Time-frequency maps of
evolution of these statistics provides a view inside peculiarites of
collective interactions between geophysical fields on different stages
of earthquake preparation in various frequency bands and time
intervals. My question is the following: do wavelets give some tools,
which are analogous to coherences, responce functions and other
statistics, describing interaction between different signals ? Is
there any articles and books on these very topic (not multidimensional
wavelets, but processing multidimensional signals by wavelets) ?
Sincerely yours, Alexey Lyubushin, Dr.Sci., Unit.Inst.Phys.Earth,
Moscow, Russia. ------- End of forwarded message -------
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Date: Thu, 02 Apr 1998 14:25:22 +0100
From: Natalya Hunter Williams <nat...@pet.hw.ac.uk>
Subject: #23 Question: Ridge and skeleton extraction
Dear all -
I am working towards a PhD in Petroleum Engineering, and have been
using wavelets (CWTs) to analyse petrophysical data for characteristic
heterogeneity lengthscales indicative of a sedimentary control (using
Matlab). I want to apply the ridge and skeleton method to extract the
hierarchical wavelength information from the data. I'm looking for
some freeware code which performs this operation. If you have some
ideas about where I might find this, I'd be very grateful if you could
let me know.
many regards
Natalya
Natalya Hunter Williams nat...@pet.hw.ac.uk
Petroleum Engineering http://www.pet.hw.ac.uk/res/rds/
Heriot-Watt University
Edinburgh EH14 4AS
Tel: 0131-451-3603 Fax: 0131-451-3127
------------------------------
Date: Tue, 7 Apr 1998 15:07:56 -0300 (EST)
From: "Nubia S.D. Brito" <nu...@shannon.dee.ufpb.br>
Subject: #24 Question: Morlet wavelet
Dear Wavelet Digest Team,
I am a PhD student at the Federal University of Paraiba, Brazil
and I am working on the application of wavelets for power system transients.
I would like to use the Morlet wavelet for this application.
The Morlet wavelet is:
g(t)=exp(j*w*t)exp(-t**2/2).
According to the wavelet literature, this function is a wavelet if
w=5.336. In this case the condition required for wavelets:
integral(g(t)dt)=0.0
is satisfied because the value obtained was 0.0000093.
Recently, a research proposed the following function for power
system transients:
h(t)=exp(-2.7*t**2)cos(1.47*t).
In this case:
integral(h(t)dt)=0.88.
I conclude that the function h(t) is not a wavelet. Am I right?
Can I change the parameters of the Morlet wavelet?
I would like to receive some informations about admissibility
condition for wavelets.
I would appreciate any information about these questions.
Thank you.
Nubia S.D.Brito.
e-mail: nu...@dee.ufpb.br
------------------------------
Date: Sat, 11 Apr 1998 16:06:14 +0100
From: Nick Pelling <nj...@globalnet.co.uk>
Subject: #25 Question: Wavelets & super-resolution of 2d images?
Dear Waveleteers,
Has anyone seen any references to wavelets' application to 2d-image
super-resolution? ie, using a wavelet decomposition of an image to
predict higher-order wavelets, and thus infer likely (but
non-existent) detail. 8^)
Thanks, .....Nick Pelling.....
------------------------------
Date: Sun, 12 Apr 1998 15:24:03 PKT
From: "Awais M. Hussain" <awais....@tes-cressoft.com.pk>
Subject: #26 Question: Error in Matlab wavelet toolbox manual?
Question:
The MATLAB wavelet toolbox manual on p.6-13 (1996) defines the DWT
of a signal s(n) as:
C(j,k) = \sum_{n \in Z} s(n) g_{j,k} (n)
with
g_{j,k}(n) = 2^{-j/2} g( 2^{-j} n - k)
where g(n) is the wavelet filter's impulse response (discrete-
time). Thus g_{j,k} are the dilations of the discrete filter?
This does not appear to be the correct representation of the DWT. Can
someone explain?
Awais
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Date: Mon, 13 Apr 1998 10:34:28 +0400
From: "CHANE-MING F." <fabrice.c...@univ-reunion.fr>
Subject: #27 Question: Ordering of Wavelet packets in Matlab wavelet toolbox?
Dear,
I'm working on the application of wavelet packets on one dimensional
signal and I would like to have some information about how to order
wavelet packet decomposition into frequency as mentionned in the
Matlab wavelet toolbox? Is there any algorithm? I thank you in
advance.=20 Please contact me.
Laboratoire de Physique de l'Atmosph=E8re =20
Universit=E9 de la R=E9union - Facult=E9 des sciences
BP 7151 - 15 avenue Ren=E9 Cassin - 97715 ST DENIS Messag Cedex 9
Tel : (0262) 93 82 39 - Fax : (0262) 93 81 66
E.Mail : fch...@univ-reunion.fr
------------------------------
Date: Thu, 16 Apr 1998 17:49:50 +0200
From: salami <tw4...@pop.vub.ac.be>
Subject: #28 Question: Gaussian Wavelets
Dear waveletters,
For my endwork I've a part about wavelets. We use gaussian wavelets
for a base (Morlet wavelets, I think). The problem now is: how do we
use gaussian wavelets bases in grids? Which leeds to following
question: when are two gaussian wavelets orthogonal? It's probably
very simple, but I need to know...
I hope you can help me or help me to help myself. It's not very simple
to find practical basic information to-the-point on wavelets.
Thanks,
Rob Lemeire
------------------------------
End of Wavelet Digest 7 Issue 4
************************************
Reposted by
Prof. Kenneth R. Jackson, k...@cs.toronto.edu
Computer Science Dept., http://www.cs.toronto.edu/~krj
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(FAX: 416-978-1931) http://www.cs.utoronto.ca/~krj
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