DOTTORATO DI RICERCA IN INGEGNERIA DELL’ INFORMAZIONE
DIPARTIMENTO DI INGEGNERIA DELL’ INFORMAZIONE
UNSER - a.a. 1999/2000
PROGRAMMA DEL CORSO:
- 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.
Lecture I: Introduction to wavelets — the signal
Lecture II: Multiresolution analysis and wavelet
bases on L_2.
Lecture III: Wavelet theory.
Applications in medicine and biology
G. Strang and T. Nguyen, Wavelets and filter banks. Wellesley, MA:
M. Unser and A. Aldroubi, "A review of wavelets in biomedical applications,"
Proceedings ofthe IEEE, vol. 84, no. 4, pp. 626-638, April 1996.
M. Unser and T. Blu, "Fractional splines and wavelets," SIAM Review,
vol. 42, no. I, pp. 43-67, March 2000.