Learning outcomes

The course deals with the wavelet transform and its applications in image and signal processing. The WT can be considered as a generalization of the Fourier transform to the time/frequency (or time/scale) analysis domain. Accordingly, it allows to overcome some of the main limitations of the FT as the analysis of transient signals that can be characterized with precisely in both the time and the frequency spaces at the same time. Multiresolution analysis is particularly suitable for natural and biological signals, feature extraction for pattern recognition, denoising and image coding.

Laboratory

The course will be complemented by lab sessions aiming at acquiring the practical instruments that are needed in this framework as well as to solve some basic problems. This will be performed using the Matlab Wavelet toolbox.

Books

- A wavelet tour of signal processing, Stephane Mallat, Academic Press (principale riferimento seguito nel corso)
- Wavelets and subband coding, Vetterli and Kovacevic, Prentice Hall

Program

1) Fundamentals of signal and image processing
- Fourier transform in 1D and 2D
- Windowed FT

2) Wavelets and pyramids
- Introduction to the WT
- Wavelet basis
- Wavelet families
- Fast discrete wavelet transform (DWT)
- 2D discrete wavelet transform
- lifting-steps implementation
- Advanced concepts
- Applicatins

3) Advanced coding systems
- Entropy, information, entropy coding
- Wavelet-based coding
- JPEG2000

4) Wavelets in biomedicine

Examination Methods

Theory

The exam consists of two parts.
The first part will concern the first part of the program (up to the 2D DWT included).
The second part can be one of the three following options:
a) Oral on the second part of the course
b) A seminar on as assigned topic
c) A project

Type of exam: oral or written, depending on the number of candidates.

Laboratory

An evaluation of the Lab activities will be performed during the classes. For those who don't take part to the lab sessions the evaluation will be performed during the exam.

Teaching materials

•   Complementi all'introduzione   (pdf, it, 725 KB, 08/03/12)
•   Elementi di sistemi e segnali   (pdf, it, 2711 KB, 15/03/12)
•   Esercitazione n. 1   (msword, it, 26 KB, 13/03/12)
•   Esercitazione n. 2   (zip, it, 2545 KB, 02/04/12)
•   Esercitazione n. 3   (docx, it, 59 KB, 13/04/12)
•   Esercitazione n. 4   (docx, it, 60 KB, 17/04/12)
•   Esercitazione n. 5   (zip, it, 897 KB, 01/05/12)
•   Esercitazione n. 6   (pdf, it, 75 KB, 04/05/12)
•   Esercitazione n. 7   (zip, it, 365 KB, 09/05/12)
•   Esercitazione n. 8   (zip, it, 1095 KB, 14/05/12)
•   Introduzione   (pdf, it, 2891 KB, 08/03/12)
•   L10 - Image Quality Assessment   (pdf, it, 2730 KB, 10/05/12)
•   L3bis: An approximation tour   (pdf, it, 870 KB, 28/03/12)
•   L3 - Wavelets and multiresolution   (pdf, it, 4899 KB, 13/03/12)
•   L4 - paper Mallat MP 1993   (pdf, it, 2482 KB, 29/03/12)
•   L4 - Wavelets and filterbanks   (pdf, it, 5708 KB, 11/04/12)
•   L5 - Wavelets in higher dimensions   (pdf, it, 2667 KB, 11/04/12)
•   L6 - Advanced concepts   (pdf, it, 2574 KB, 17/04/12)
•   L7 - Lifting wavelets   (pdf, it, 3006 KB, 19/04/12)
•   L8 - Subband Coding   (pdf, it, 2582 KB, 25/04/12)
•   L9 - JPEG2000   (pdf, it, 1162 KB, 10/05/12)
•   Lezione 2   (pdf, it, 1890 KB, 08/03/12)
•   Lezione Seminariale n. 1   (pdf, it, 7739 KB, 03/04/12)
•   Lezione Seminariale n. 2   (pdf, it, 19186 KB, 11/04/12)
•   Scheduling lezioni seminariali   (pdf, it, 36 KB, 25/04/12)