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

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.

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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

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

 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

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

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 
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
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:




  This new software is still being developed. Comments, suggestions and 
  bug reports will be greatly appreciated. The mail address for reports is  

  The programs included in the toolbox are :
    (A more extensive repport will be included in the ftp server)

   * KMWT: The Multilevel Wavelet Transform. Supports the multiscale
  	  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
  		- 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 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

--------------------------- 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:

                     (directory: pub/Uvi_Wave/matlab/)

                     (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 :

                         Nuria Gonzalez Prelcic
                         Sergio J. Garcia Galan

            Departamento de Tecnologias de las Comunicaciones
                           Universidad de Vigo

--------------------------- 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
 * 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
 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).
                                                 Metin Akay, Ph.D.
                                                 Workshop Chair
         17th Annual International Conference of IEEE EMBS
     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.


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

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

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


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

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

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 ?


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

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 

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 
If someone knows preprints, papers, books on this subject, please 
send the reference to

    in particular we are looking for
    A. Arneado, E. Bacry, AND J. F. Muzy `Wavelet analysis of fractal 
signals', preprint, September 1991

    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

Many thanks


--------------------------- Topic #18 -----------------------------------
From: rannou@cs.utk.edu
Subject: Question: Looking for code with non power of 2 length signals

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
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.

--------------------------- 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 :

Feel free to connect and to send us your comments.

-------------------- End of Wavelet Digest -----------------------------