CRN 15050
From Classes
Syllabus
- Topic. Applied Mathematics: Discrete Wavelets and Image Processing.
- Time and Place. TR 17:00-18:20 in Bell 130
- Instructor. Helmut Knaust, Bell Hall 219, hknaust@utep.edu, 747-7002
- Office Hours. TR 14:00-15:00, after class, or by appointment.
- Textbook. Patrick Van Fleet. Discrete Wavelet Transformations: An Elementary Approach with Applications. Wiley-Interscience.
- 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 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 40 years. During the course you should expect (and I will expect) that you make considerable progress in the following areas:
- Develop an understanding of the theoretical underpinnings of wavelet transforms and their applications.
- Learn how to use a computer algebra system for mathematical investigations, as a computational and visualization aid, and for the implementation of mathematical algorithms.
- Get a flavor of the ideas and issues involved in applying mathematics to a relevant engineering problem.
- 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 presented in class by student volunteers. 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: Tuesday, October 4, and Thursday, November 17. Each exam counts 20% of your grade.
- Projects. You will complete several individual 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 during finals week. The final project will count 30% of your grade.
- Mathematica. Mathematica is installed on many lab computers at UTEP. You can also access the program remotely from home via https://my.apps.utep.edu/vpn/index.html; alternatively you can request a home license (see http://admin.utep.edu/Default.aspx?tabid=74264). A nice introduction to Mathematica can be found at An Elementary Introduction to the Wolfram Language, by Stephen Wolfram.
- 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.
- Drop Policy. The class schedule lists Friday, October 28, 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 classroom accommodations, please contact The Center for Accommodations and Support Services (CASS) at 747-5148, or by email to cass@utep.edu, or visit their office located in UTEP Union East, Room 106. For additional information, please visit the CASS website at sa.utep.edu/cass.
- Academic Integrity. All students must abide by UTEP's academic integrity policies, see http://sa.utep.edu/osccr/ for details.
Mathematica notebooks
Homework
- 11/8: Problem 8.2
- 10/25: Problems 5.19a, 5.20, 5.23, 5.27
- 10/6: Exercises 1-6 in Multi-Resolution Analysis for the Haar Wavelet.
- 9/29: Problems 4.22, 4.25, 4.28, 4.33, 4.34ab. [Problem 4.34(b) seems to be wrong - try \(\overline{c_k}\) instead.]
- 9/27: Compute the complex Fourier coefficients for \(f(t)=|t|\), then write the answer in terms of sine and cosine.
- 9/13: Problems 3.16, 3.22, 3.23, 3.26, 3.27, 3.35, 3.37, 3.40, 3.43.
- 9/6: Problems 3.6, 3.8.
- 8/25: Problems 2.10b, 2.12b, 2.13, 2.22, 2.27.
Projects
Final Projects | Project 4, due November 10. | Project 3, due October 20. | Project 2, due September 22. | Project 1, due September 8.
Materials
Introduction | Mathematica Tips, Tricks, and Techniques, by Michael A. Morrison | Images (zip file) | Fourier Series Using Trigonometric Functions (www.sosmath.com) | Multi-Resolution Analysis for the Haar Wavelet (New version) | Computing the Daubechies-4 Coefficients | Presentation: Smoke Detection