CRN 16332

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  • Topic. Discrete Wavelets and Image Processing
  • Time and Place. MW 18:30-19:50 in Bell 130A
  • Instructor. Helmut Knaust, Bell Hall 219,, 747-7002
  • Office Hours. M 17:30-18:20, R 11:00-12:00, after class, or by appointment.
  • USB Stick. Please bring an initially empty USB stick with at least 1 GB capacity to all class meetings.
  • Prerequisites. The course has a very applied flavor. Knowledge of fundamental Calculus is required; some limited familiarity with matrices may be helpful. You will use Mathematica extensively, but prior knowledge is not expected. On the other hand, this is an advanced mathematics course, so you should have some mathematical maturity.
  • Course Objectives. We will study a recent topic in mathematics (discrete wavelets), and how it is applied to the practical problem of image processing and compression. While some of the underlying ideas go back to Joseph Fourier (1768-1830) and Alfred Haar (1885-1933), most of the material you will see is not older than 30 years. During the course you should expect (and I will expect) that you make considerable progress in the following areas:
  1. Develop an understanding of the theoretical underpinnings of wavelet transforms and their applications.
  2. Learn how to use a computer algebra system for mathematical investigations, as a computational and visualization aid, and for the implementation of mathematical algorithms.
  3. Get a flavor of the ideas and issues involved in applying mathematics to a relevant engineering problem.
  4. Be able to give and defend a mathematical presentation to a group of your peers.
  • Class Participation and Homework. I will regularly assign homework. The homework will not be collected, but discussed in class. You are expected to always actively participate in class. Your homework and participation grade will contribute 10% to your grade.
  • Tests. Two exams will be given on the following dates: Wednesday, September 29 and Monday, November 8. Each exam counts 20% of your grade.
  • Projects. You will complete several programming projects. Some class time will be dedicated to work on these projects. These projects will be graded and contribute a combined total of 20% to your grade.
  • Final Project. Small groups of students will prepare and present a comprehensive final project at the end of the semester. The final project will count 30% of your grade.
  • Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing homework and project assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.
  • Attendance. You are strongly encouraged to attend class. Students with four absences (excused or unexcused) will be dropped from the course with a grade of "F".
  • Drop Policy. The class schedule lists Friday, October 29, as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F".
  • Students with Disabilities. If you have a disability and need special accommodation, please contact the Disabled Student Services Office (DSSO) in Union East 106, 747-5148,




Open problems

Exercise 5.

  • 10/18: MRA handout, Exercises 1-6.
  • 10/6: Problems 5.4, 5.5, 5.10, 5.14, 5.15, 5.20, 5.25
  • 9/27: Problems 4.22, 4.25, 4.28, 4.33, 4.34. [Problem 4.34(b) seems to be wrong - try \(\overline{c_k}\) instead.]
  • 9/22 (1) Compute \(\langle \cos (nt), \cos (nt)\rangle\) for all \(n=0,1,2,\ldots\). (2) Find the Fourier sine and cosine coefficients for the function \(\displaystyle{f(t)=\begin{cases} -1& (0\leq t \leq \pi)\\1& (-\pi\leq t <0)\end{cases}}\).
  • 9/13: Problems 3.22, 3.23, 3.26, 3.27, 3.35, 3.37, 3.40, 3.43.
  • 8/25: (1) Problems 2.10b, 2.12b, 2.13, 2.22, 2.27. (2) Work through First Five Minutes with Mathematica: Open the program, go to Help->Documentation Center->First Five Minutes with Mathematica; alternatively watch the screencast video at


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