ECE 544-MD: "Wavelets in Signal Processing"
Fall 2007
Instructor:
Lectures: Tuesdays and Thursdays, 10:00 - 11:20 am; 252 Mechanical Engineering Bldg.
Office hours: Tuesdays 2-3 pm (115 CSL) + appointments by email.
Teaching Assistant:
Office hours: Wednesdays 3-4 pm (330A EL) + appointments by email.
Handouts:
Homework:
Course description:
Wavelets have established themselves as an important tool in modern signal processing as well as in applied mathematics. The objective of this course is to establish the theory necessary to understand and use wavelets and related constructions. A particular emphasis will be put on constructions that are amenable to efficient algorithms, since ultimately these are the ones that are likely to have an impact. We thus study applications in signal processing, communications, and sensing where time-frequency transforms like wavelets play an important role. The course has computer and research projects involving independent study.
Text books:
Required:
- M. Vetterli, J. Kovacevic, and V. K. Goyal, "The World of Fourier and
Wavelets: Theory, Algorithms and Applications," (manuscript); available for purchase from the IEEE store in Everitt Lab;
downloadable from http://www.fourierandwavelets.org.
OR
M. Vetterli and J. Kovacevic, "Wavelets and Subband Coding," Prentice
Hall, 1995; downloadable from http://www.waveletsandsubbandcoding.org
- Research papers.
Recommended:
- S. Mallat, "A Wavelet Tour of Signal Processing," Academic Press,
Second Edition, 1999.
- G. Strang and T. Q. Nguyen, "Wavelets and Filter Banks," Wellesley-Cambridge
Press, Revised Edition, 1998.
- I. Daubechies, "Ten Lectures on Wavelets," SIAM, 1992.
- P. P. Vaidyanathan, "Multirate Systems and Filter Banks," Prentice
Hall, 1993.
Lecture Topics:
1. Introduction and Background (6 hours)
a. Why wavelets, filter banks, and multiresolution
analysis?
b. Signal spaces and operators
c. Review of Fourier theory
d. Multirate signal processing
e. Time-frequency analysis
2. Discrete-Time Bases and Filter Banks (8 hours)
a. Series expansions of discrete-time signals
b. Analysis and design of filter banks
c. Orthogonal and biorthogonal filter banks
d. Tree-structured filter banks
e. Discrete wavelet transform
3. Continuous-Time Bases and Wavelets (8 hours)
a. Multiresolution analysis
b. Iterated filter banks
c. Wavelets and filter banks
d. Wavelet series and its properties
e. Regularity and approximation properties
4. Overcomplete Expansions and Continuous Transforms (5 hours)
a. Frame theory
b. Oversampled filter banks
c. Continuous wavelet and short-time Fourier transforms
5. Advanced Topics (9 hours)
a. Sparse representation
b. Linear and non-linear approximation in various bases
c. Non-linear signal estimation
d. Multidimensional filter banks and wavelets
e. Multiscale geometric representation and processing
f. Compressed sensing
6. Applications (9 hours)
a. Speech, audio, image, and video compression
b. Signal denoising
c. Feature extraction
d. Inverse problems
Grading:
- Homework: 25%
- First midterm: 25%
- Second midterm: 25%
- Final project: 25%
Wavelet papers:
- Wavelets,
by G. Strang, American Scientist 8 (April 1994)
250-255.
- Wavelets and signal processing, by O.
Rioul and M. Vetterli, IEEE Signal Processing Magazine, vol. 8, no.
4, Oct. 1991, pp. 14-38.
- A
theory for multiresolution signal decomposition: the wavelet
representation, by S. Mallat, IEEE Transaction on Pattern Analysis
and Machine Intelligence, vol. 11, p. 674-693, July 1989.
- Wavelets and filter banks: theory and design,
by M. Vetterli and C. Herley, IEEE Transactions on Signal
Processing, vol. 40, Sep. 1992, pp. 2207-2232.
- Wavelets,
approximation and compression, by M. Vetterli, IEEE Signal
Processing Magazine, vol. 18, no. 5, Sep. 2001, pp. 59-73.
- Theoretical
foundations of transform coding, by V. K. Goyal,
IEEE Signal Processing Mag., vol. 18, no. 5, pp. 9-21, Sept.
2001.
Wavelet links:
