EPFL | Biomedical Imaging Group | Wavelets and Applications

Wavelets and Applications

M. Unser

Series of Invited Lectures, Information Engineering Department, University of Siena, Italian Republic, July 5-7, 2000.

Wavelets provide a new way of decomposing signals or images into their elementary constituents across scale (multi-resolution decomposition). They provide a one-to-one representation (orthogonal transform) in very much the same way as the Fourier transform, except that the basis functions are now localized in both time (or space) and frequency. Wavelets have many remarkable properties and are extremely versatile. During the past few years, they have being tried on many problems in different areas of applied mathematics and engineering, often with good success.

In this series of lectures, I will present the basic signal processing and mathematical principles behind wavelets. I will also introduce the students to the more advanced aspects of wavelet theory. I will discuss applications in biomedical image processing.

Course Content

Lecture 1: Introduction to Wavelets—The Signal Processing Perspective
Lecture 2: Multiresolution Analysis and Wavelet Bases of L₂
Lecture 3: Wavelet Theory. Applications in Medicine and Biology

References

G. Strang, T. Nguyen, Wavelets and Filter Banks, Wellesley MA, Wellesley-Cambridge, 1996.
M. Unser, A. Aldroubi, "A Review of Wavelets in Biomedical Applications," Proceedings of the IEEE, vol. 84, no. 4, pp. 626-638, April 1996.
M. Unser, T. Blu, "Fractional Splines and Wavelets," SIAM Review, vol. 42, no. 1, pp. 43-67, March 2000.

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser0003.html,
AUTHOR="Unser, M.",
TITLE="Wavelets and Applications",
BOOKTITLE="Series of Invited Lectures",
YEAR="2000",
editor="",
volume="",
series="",
pages="",
address="Siena, Italian Republic",
month="July 5-7,",
organization="University of Siena, Information Engineering
	Department",
publisher="",
note="")

© 2000 University of Siena. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from University of Siena. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.