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42-703/18-799: Wavelets and Multiresolution Techniques [syllabus]

The instructor for this course is Jelena Kovačević.

The course will meet for one session each week.

Course date and times: Wed, 4:30-7:20pm, Baker Hall 255A.

Instructor’s office hours: Wed, 3:30-4:30pm, Hamerschlag Hall C121 (map)

Contacting the Instructor: The best way to contact me is by email (jelenak at cmu dot edu). Putting "42-703" or "18-799" in the Subject line guarantees a faster response from me.

TA: Aliaksei Sandryhaila.

TA’s office hours: Thu, 2:00-3:00pm, Porter Hall B8.

All course material will be posted at this site. Lecture topics can change without notice depending on the students enrolled and their backgrounds. A prerequisite for this course is 18-396 Signals and Systems or equivalent.

 

Course Schedule
(tentative and subject to change)

01/16/07
Chapter 0: Multiresolution Overview
Chapter 1: From Euclid to Hilbert (Part 1)

[slides]

 

01/23/07
Chapter 1: From Euclid to Hilbert (Part 2)

 

01/30/07

Chapter 1: From Euclid to Hilbert (Part 3)

 

02/06/07
Chapter 1: From Euclid to Hilbert (Part 4)

 

02/13/07

Chapter 2: Sequences and Signal Processing

 

02/20/07

Chapters 3: Fourier’s World and Sampling

 

02/27/07

Chapter 5: Time, Frequency, Scale and Resolution

 

03/05/07

Chapter 6: Filter Banks: Building Blocks of Time-Frequency Expansions

 

03/12/07
No Class: Spring Break

 

03/19/07

Chapter 6: Filter Banks: Building Blocks of Time-Frequency Expansions

 

03/26/07

Midterm

 

04/02/07

Chapter 7: Wavelet Series on Sequences 

 

04/09/07

Chapter 10: Frames on Sequences

 

04/16/07

Chapter 8: Wavelet Series on Functions
Chapter 9: Localized Fourier Series on Sequences and Functions

Chapter 11: Continuous Wavelet and Windowed Fourier Transforms

 

04/23/07
Paper 1 Presentation
Team: Chuangsuwanich, Iranoppaiboon

[notes]

Paper 2 Presentation
Team: Ramzi, Muneomoto, Boddeti

[notes]

 

 

04/30/07
Paper 3 Presentation
Team: Tarpeh, Robinson, Lawrence

[notes]

Paper 4 Presentation
Team: Wang

[notes]

Project Presentation
Team: Hoffman
[notes]

 

Homeworks and Midterm

 

Problems

Solutions

Homework 1

1.19-1.23

download

Homework 2

1.1-1.10 (choose 5)

download

Homework 3

1.11-1.12 (choose 1)
1.13-1.14 (choose 1)
1.15-1.16 (choose 1)
1.17-1.18 (do both)

download

Homework 4

2.1-2.11 (choose 5)

download

Homework 5

5.1-5.9 (choose 5)

download

Homework 6

6.1-6.9

download

Homework 7

 

download

Homework 8

 

download

Homework 9

 

download

Midterm

download

download

 

Notes

Title

Last update

Front matter

04/01/08

Back matter

04/01/08

Chapter 0

04/01/08

Chapter 1

04/01/08

Chapter 2

04/01/08

Chapter 3

04/01/08

Chapter 4

04/01/08

Chapter 5

04/01/08

Chapter 6

04/01/08

Chapter 7

 

Chapter 8

 

Chapter 9

 

Chapter 10

 

Chapter 11

 

 

Projects

You will be assigned a topic with a “main paper” (MP). Your task will be to:

1.    Read that paper in detail, understand it, understand any derivations/math that might be in it.

2.    Find at least one paper citing the MP and read and understand that one. The second paper (or more) could be an application of the theory in the MP, any further developments along the lines of the MP, any generalizations/improvements of the MP.

3.    You will give a class lecture on the topic in April (we will do a random drawing to see who goes when).

4.    You will be expected to write a 4-page conference-style paper (templates) covering the topic you were assigned. You will discuss the MP as well as the other paper(s) you covered.

You will be graded on: (1) your presentation in class (50% of the project grade = 25% of the overall grade) and (2) your final paper (50% of the project grade = 25% of the overall grade). You will be working in a team of people. Note also that while one team will be presenting, all other students are supposed to read the MP before the class as I will be grading everyone on their participation. Below are the topics:

1.    Filter Banks

MP: M. Vetterli. Filter banks allowing perfect reconstruction. Signal Proc., 10(3):219–244, Apr. 1986.

 

2.    Wavelet Packets

MP: K. Ramchandran and M. Vetterli. Best wavelet packet bases in a rate-distortion sense. IEEE Trans. Image Proc., 2(2):160–175, Apr. 1993.

 

3.    Local Discriminant Bases

MP: N. Saito and R. Coifman. Local discriminant bases and their applications. Journ. Math. Imag. Vis., 5:337–358, 1995.

 

4.    Wavelets in Microscopy

MP: B. Forster, D. Van De Ville, J. Berent, D. Sage, M. Unser, Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images, Microscopy Research and Technique, vol. 65, no. 1-2, pp. 33-42, Sep. 2004.

Last modified: Apr 1 2008