MATH 672-001/CSI 746-001 - Wavelet Theory - Fall 2003


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.

Course syllabus pdf, postscript, html

Class Notes

Sections 5.1-5.3
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:
DHT of a function with a jump
2D DHT demo
2D DHT reconstructions
makeimage (needed to display the images generated in the above 2 demos)
 Cascade Algorithm

Solutions to Homework sets

Homework #1
Homework #2
Homework #3
Homework #4
Homework #5

Math Department.
Computer Lab Hours.

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:
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.

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.

A comprehensive list of wavelet links may be found at the Wavelet Digest homepage maintained by Wim Sweldens.

To contact me, send mail to: