DOTTORATO DI RICERCA IN INGEGNERIA DELL’ INFORMAZIONE

DIPARTIMENTO DI INGEGNERIA DELL’ INFORMAZIONE

PROF. MICHAEL 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
processing perspective

**Lecture II: **Multiresolution analysis and wavelet
bases on L_2.

**Lecture III: **Wavelet theory.
Applications in medicine and biology

**References: **

G. Strang and T. Nguyen, Wavelets and filter banks. Wellesley, MA:
Wellesley-Cambridge, 1996.

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.