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## Revision as of 18:54, 19 August 2008

## Contents

## EE 596, Wavelets, Fall 2008

**Course Description:** The theory and application of wavelet decomposition of signals. Includes subband coding, image compression, multiresolution signal processing, filter banks, and time-frequency tilings.

**Prerequisites:** *EE 483, Introduction to Digital Signal Processing*, or equivalent course. Please note that the course will assume some knowledge of standard DSP concepts as well as of some basic linear algebra. If you took these two courses some time ago it would be a good idea to review some of the key material early in the semester.

**Recommended Preparation:** *MATH 599, Introduction to Wavelets*, and *EE 569, Introduction to Digital Image Processing*. None of these courses is required.

## Instructor

*Signal and Image Processing Institute*

*Department of Electrical Engineering*

*University of Southern California*

*3740 McClintock Ave., EEB 436*

*Los Angeles, CA 90089-2564*

*Tel: (213) 740-2320*

*Fax: (213) 740-4651*

*Email: antonio DOT ortega AT sipi DOT usc DOT edu*

## Schedule

**Lectures**Tuesday and Thursday, 2-3:30pm, OHE 100**Office hours**TBA, EEB 436, and by appointment.**Teaching Assistant**Godwin Shen- Email: godwinsh AT usc DOT edu
- Office Hours: TBA, EEB 441.

**Grader**TBA**Midterm 1**TBA**Midterm 2**TBA

## Grading

There will be two midterms (dates TBD). Each midterm will account for 30% of the grade. The remaining 40% will be based on homeworks and a project. There will be around 4 homeworks and the project will be due at the end of the semester.

## DEN Access

This semester I will use the Blackboard system offered by DEN to post assignments and solutions, as well as grades. Please register with DEN and create your DEN profile as soon as possible by following the instructions on the DEN Webpage.

## Texbooks

**Required:**

- Martin Vetterli and Jelena Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995. This textbook is now available electronically at http://www.waveletsandsubbandcoding.org
- Matlab Wavelet Toolbox, This toolbox is available on the student computer accounts.

**Recommended:**

- Gilbert Strang and Truong Q. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, 1995
- P. P. Vaidyanathan, Multirate Systems and Filter Banks , Prentice Hall, 1993

## Material Covered (Subject to Change)

**Weeks 1 and 2**Introduction and Motivation. Signal representation using bases. Hilbert spaces. Orthogonal, bi-orthogonal basis and overcomplete expansions. Example: representing finite energy continuous signals using Haar basis. Example of construction of Haar basis**Week 3**Bases for discrete signals. Finite and infinite dimensional spaces.**Week 4**Overcomplete expansions. Searching for the best representation. Matching pursuits and variations. Compressed sensing.**Weeks 5 and 6**Multirate signal processing. Filterbanks and discrete wavelet transforms. Time domain, frequency domain and polyphase domain representations.**Week 7 and 8**2-Channel orthogonal filterbanks. Iterated filterbanks. Bi-orthogonal filterbanks. Lifting factorizations. Multichannel filterbanks. Modulated filterbanks.**Weeks 9 and 10**Multidimensional wavelets. Edgelets, bandlets, ridgelets and other extensions. Lifting for video representation.**Week 11**Continuous time wavelets. Series expansions of continuous signals. Haar, Sinc, Meyer, Daubechies and Spline wavelets. Mallat algorithm.**Weeks 12 and 13**Applications. Compression. Classification. Graphics.

## Projects

- Project requirements:
- Projects should be done individually.
- Each project must involve using the wavelet transform as a tool. A signal is analyzed/classified, etc by computing its wavelet transform and then the required task (e.g. denoising/classification) is performed in the transform domain.
- The Matlab toolbox or C libraries can be used for the project. C libraries are available at Dartmouth and Rutgers.
- Whichever method is used, the source code will have to be made available along with the project report (only for the routines that you write, which could call those available in matlab or C.)

- Reporting requirements: a final report and a class presentation.
- Project descriptions and references
- Test data for the projects
- Software packages

Demos on the web

- Jelena Kovacevic's webpage contains numerous pointers to books, projects, demos, applets, etc.
- Wavelet Library Demo at South Carolina
- Bell Labs: Wim Sweldens' Wavelet Cascade Applet
- Biomedical Group at EPFL - Fractional Splines Demo
- Texture Classification Demo
- SIMPLIcity Content Based Image Retrieval - Search
- Wavelet-Based View Synthesis
- More links...
- A measure of Wavelet popularity?

## Sample Project Topics (from Fall'01) - Organized by Areas

- Coding
- Implementation of a Pyramidal Image Coder
- Compression of finite-length discrete-time signals using flexible adaptive wavelet packets<
- Wavelet Descriptors for Planar Curves
- Sinusoidal Modeling of Audio Signals Using Frame-Based Perceptually Weighted Matching Pursuits
- Low Complexity Motion Estimation Algorithm for Long-term Memory Motion Compensation Using Hierarchical Motion Estimation
- Global/Local Motion Compensation for 3D Video Coding Based on Lifting Techniques

- Classification/Recognition
- Shift Invariant Texture Classification by Using Wavelet Frame
- Texture Feature Extraction with Non-Separable Wavelet Transforms
- Comparison of Two Wavelet-Based Image Watermarking Techniques
- Application of Wavelet Transform in Analysis of Fractal Signals
- Human-Face Detection and Location in Color Images Using Wavelet Decomposition
- Music/Speech Classifier using Wavelets
- Wavelet Decomposition for the Analysis of Heart Rate Variability
- Wavelet-based fMRI dynamic activation detection
- Wavelet analysis of evoked potentials
- Detection of Microcalcifications in Mammograms using Wavelet Transforms
- Wavelet-based Tone Classification for Thai

- Denoising
- Comparison of Denoising via Block Weiner Filtering in Wavelet Domain with Existing Ad-hoc Linear and Non-linear Denoising Techniques
- Wavelet-domain filtering of data with Poisson noise
- Contrast Enhancement and De-noising using Wavelets
- Wavelet Denoising Applied to Time Delay Estimation
- Comparison of image denoising using Wavelet Shrinkage vs. MMSE using an exponential decay autocorrelation model
- Threshold Denoising Effects on Covariance Matrices
- Comparing Performance of Different Wavelet De-noising algorithms with Basic Noise Removal Techniques
- Information Driven Denosing of MEG data in the Wavelets Domain
- Two Methods for Image Enhancement

- Watermarking/Halftoning
- Introduction of IWT to wavelet-based watermarking and its effect on performance
- Inverse Halftoning using Wavelets

- Communications
- Wavelets Based MC-CDMA System
- MMSE Estimation Multi-user detection for CDMA System based on Wavelet Transform