MATH 672-001/CSI 746-001 - Wavelet
Theory - Fall 2003
Announcements:
Errata for Walnut, "An Introduction to
Wavelet
Analysis"
Project proposals. The final
project write-up is due at the beginning of class on Thursday Dec.
11. What I am expecting is a write-up of everything you have
learned in researching your project. You should include details
and all background information. Assume that you are writing a
document for a wavelets novice. what I want to be able to do in
reading your write-up is to move seamlessly from a description of the
application to a description of how wavelets might be useful for the
application. If your project is not about a specific application
of wavelets, but is more mathematical, I want to understand why this
particular aspect or extension of wavelet theory is interesting to you
and why it is important, and how it relates to some of the wavlet
theory we have discussed in class.
Guidelines for giving your project presentations:
1. You will have 15 minutes for your presentation.
Please keep to this time limit. I will be ruthless
in enforcing this rule. I will have a timer with me that will indicate
when
15 minutes are up. At that time you will have exactly 60 seconds to
wrap up. After that time you will be cut off.
2. Choose one main point to make for your talk. Do
not attempt
to review your entire project. Include the details for me to see in the
write-up. Choose one interesting aspect of your project to present to
the class. Remember the time limit.
3. Remember your audience. You have all seen the
basics of wavelet theory. There is no need to include exposition about
what we have already done in class in your talk. If there is to be
exposition in your talk, let it be about aspects of your project that
may not be familiar to many of the class members.
4. Practice your talk beforehand. This will help you be
less nervous (if you are inclined to be anyway) and also will help you
keep to the time limit.
5. Use overhead transparencies or PowerPoint. This is the
preferred method of giving a talk like this. Writing everything on the
board will take too much time. The cardinal rule here is to not clutter
your transparencies or PowerPoint pages with too much information. With
such talks less is more! It should be
possible to set up Powerpoint on the PC in the lecture
room. It is definitely possible to plug your laptop into the
projector. If you are planning to use any technology of this type
for your presentation, let me know in advance so we can make sure it
works for the presentation. Software
or hardware glitches are not an option!
Good luck to all of you. I am looking forward to your presentations.
Computer Account. We are going to
be
using the MATLAB Wavelet Toolbox. Therefore, you will need access to
this
Toolbox. If you already have access to this Toolbox, then you need do
nothing
else. If you do not, you should
get
an account on gauss.
Class Notes
Sections
5.1-5.3
Section5.4
Section6.1
Section6.2
Section1.1-1.2
Section2.1,2.3
Section3.1-3.8
Section4.1-4.3
Chapter 7
Chapter 8
Chapter 9
Class Notes 09-11-03
Class Notes 09-25-03
Class Notes 10-02-03
Class Notes 10-09-03
Class Notes 10-16-03
Class Notes 10-23-03
Class Notes 10-30-03
Class Notes 11-06-03
Class Notes 11-13-03
Class Notes 11-20-03
Homework Assignments:
Homework #1 (due 9-25-03):5.18, 5.20, 5.27,
5.28,
5.32, 5.33
Exercises 5.28 and 5.33 are numerical in
nature.
I recommend that you use MATLAB to do them using the MATLAB wavelet
toolbox
and the in-class MATLAB demos as a guide. But you may use any software
you like. It is sufficient just to turn in your output,
accompanied
by your observations and conclusions as called for in the exercises.
Homework #2 (due 10-2-03): 1.18, 1.46
(a)-(c),
2.22, 2.24 (c), (d), 2.60, 2.63.
Homework #3 (due 10-30-03): 3.4, 3.5, 3.6, 3.31, 3.44, 3.46
Homework #4 (due 11-13-03) 8.15, 8.17(b), (c), 8.19, 8.26, 8.43,
8.46
Homework #5 (due 12-4-03) 9.23, 9.24, 10.35, 10.37
Some MATLAB stuff:
Solutions to Homework sets
Help with MATLAB.
About the project
What your project should be like.
Your semester project should fall into one of
two
categories:
(1) Development of some mathematical aspect of
wavelet
theory not covered already in class;
(2) Exposition of some application of wavelet
theory
also not covered already in class.
Projects of both kinds can overlap with class
material
but must extend it in some significant way.
Details can be worked out with me.
What I am expecting.
Your project should consist of two parts:
(1) a write up of approximately 15 pages, and
(2) a 20-minute presentation of your project for
the class
It is recommended that you use transparencies
for
the presentation.
I believe that PowerPoint is available on the
classroom
computer.
If you want to do it this way, we will need to
make
sure that the correct software is in place well in advance.
Guidelines on the presentation are below.
Some project ideas.
There are some ideas for possible projects in
the
appendix to the textbook entitled: Excursions in Wavelet Theory.
Some of the more appropriate ones are listed
below:
- M-band wavelets
- Wavelets with rational non-integer
dilation factor
- Local Cosine Bases
- Non-MRA Wavelets
- The Lifting Scheme
- Multi-scale Edge Detection
Another possibility is the following.
Chapter 13 of the book describes the BCR algorithm in the context
of two examples of integral operators:
Sturm-Liouville Boundary Value Problems, and The Radon Transform.
Implementation and experimentation with the BCR algorithm in relation
to some of these operators would be very interesting.
Again, see me for details.
About the presentations.
- Choose one main point to make for your
talk. Do not attempt to review
your
entire project. Include the details for me to see in the write-up.
Choose
one interesting aspect of your project to present to the class.
Remember
the time limit of 20 minutes.
- Remember your audience. You all will
have seen the basics of wavelet
theory.
There is no need to include exposition about what we have already done
in class in your talk. If there is to be exposition in your talk, let
it
be about aspects of your project that may not be familiar to many of
the
class members.
- Practice your talk beforehand. This
will help you be less nervous (if
you
are inclined to be anyway) and also will help you keep to the time
limit.
- Use overhead transparencies. This is
the preferred method of giving a
talk
like this. Writing everything on the board will take too much time. The
cardinal rule here is to not clutter your transparencies with too much
information. With transparency talks less is more! Also, it is possible
to set up Powerpoint on the PC in the lecture room. If you want
to
do this, you must let me know well in advance. You may need to
supply
your own software.
Links to wavelet books:
The MathWorks MATLAB Wavelet Toolbox:
The MATLAB Wavelet
Toolbox, from The MathWorks,
provides a comprehensive collection of M-files and GUI based tools for
examining local, multiscale, and nonstationary phenomena. Wavelet
methods
offer additional insight and performance in any application where
Fourier
techniques have been used. The toolbox is useful in many signal and
image
processing applications, including speech and audio processing,
communications,
geophysics, finance, and medicine.
To contact me, send mail to: dwalnut@gmu.edu.