|
Department of Electrical Engineering
EE 5263 Topic: Digital Signal Processing:
Orthogonal Transforms, Wavelets and Fractals
(Credit 3)
The purpose of this course is to describe an applications-oriented unified model for efficient, compact representation of signals and images. The wavelet and fractals have been perhaps the most exciting development in the last decade to bring together researchers in several different fields such as signal and image processing, communications, computer science, and mathematics. The combination of brilliant theory, efficient algorithms, and successful applications makes the field of orthogonal transforms, wavelets, and fractals quite exciting. Converge originates with classical orthogonal representations and proceed through wavelets decomposition. It continues with fractal representation. Application is geared towards image compression standards, de-noising, image enhancement, watermarking, and steganography.
Textbooks: A. Boggess and J Narciwich, "First Course in Wavelets with Fourier Analysis", Prentice Hall, ISBN: 0-13-0220809-5
References:
- Alan V. Peter Wayner, Disappearing Cryptography Information Hiding: Steganography and Watermarking, Morgan Kaufmann Publishers, 2nd edition (May 2002 ISBN: 1558607692
- David F. Walnut, An Introduction to Wavelet Analysis, Birkauser Boston Second, 2002, ISBN: 0817639624
- Yao Wang, Jorn Ostermann & Ya-Qin Zhang, Video Processing and Communicatoins, Prentice Hall, 2002, ISBN 0-13-017547
- Agaian’s Lecture Notes
Prerequisites by topic: Linear Systems
Intended Audience: The course should be of interest to students working in all areas of signal and image processing, speech analysis, astronomy, biology, computer graphics, acoustics, medicine, information security, and seismology.
Coordinator: Sos Agaian, Ph.D., Professor of Electrical Engineering.
Classes: 7:00 pm-8:15pm, MS 2.02.48
Office Hours: M,W 5:00-6:00 PM., after class or by appointment
Email: sagaian@utsa.edu
Homepage: http://engineering.utsa.edu/~sagaian/
Benefits: This course will help: to understand orthogonal transforms: such as Fourier, Cosine, Sine, Hartley, Haar, Slant, and Walsh; to apply Short-time Fourier and Gabor transforms; to understand the basic principles of wavelet and subband decomposition; to understand Fractals Fractal Dimension, Iterated Function Systems, Collage theorem; to see relationships among various decomposition methods; to use fast orthogonal transforms and efficient fractal construction algorithms, to describe international compression standards: JPEG, H.261 and MPEG, to learn a basic watermark and steganalysis, and signal and image de-noising techniques.
Course Objectives: This course will help the students to:
- Understand the following orthogonal transforms: Fourier, Cosine, Haar, Slant, and Walsh;
- Implement the fast orthogonal transforms: Fourier, Cosine, Haar, Slant and Walsh;
- Understand the short-time orthogonal transforms;
- Understand the basic principles of one and two dimensional wavelets and subband decomposition;
- Understand the international compression standards JPEG, JPEG2000, H.261 and MPEG
- Understand fractal: Iterated Function Systems, Fractal dimensions
- Learn a basic watermarking, steganography, and steganalysis and signal and image de-nosing techniques.
Topics:
- Orthogonal transforms: Fourier, Cosine, Sine, Hartley, Haar, Slant, Walsh, and Short-time orthogonal transforms;
- image and video international compression standards: JPEG, JPEG2000, H.261, and MPEG;
(Project 1-presentation and report)
- Subband decompositions;
- 1.D and 2D Wavelets: construction, properties, decomposition and reconstruction, multiresolution analyses.
(Project 2-presentation and report)
- Fractals, Fractal Dimensions, Iterated Function Systems: Collage theorem;
- Filtering and compression via wavelet and fractal;
- fast orthogonal transforms and wavelets and watermarking, secure multimedia information dissemination, and steganography
(Project 3)
Performance Criteria:
Objective 1: The students will demonstrate knowledge of the basic principles of Orthogonal transforms, wavelets, and fractals.
Objective 2: The students will have a practical understanding of the basic principles of signal and image de-nosing, compression, watermarking, and steganalysis.
Objective 3: The students will have an ability to work effectively in multi-disciplinary teams
Objective 4: The students will have an ability to present technical information clearly in both oral and written formats.
Grading: The project will be graded upon based on: the level of involvement of these methods, the complexity of the project, and the level of success of the project.
|
