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 (only in case of diploma work)

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 e documents

•   L1 - Complements to Introduction   (pdf, it, 725 KB, 10/03/13)
•   L1 - Introduction   (pdf, it, 4806 KB, 10/03/13)
•   L2 - Time-meets-frequency   (pdf, it, 1841 KB, 10/03/13)
•   L3b - Wavelet packets   (pdf, it, 1260 KB, 25/03/13)
•   L3c - Matching pursuit   (pdf, it, 891 KB, 05/04/13)
•   L3 - Wavelets and multiresolution   (pdf, it, 6614 KB, 25/03/13)
•   L4 - Wavelet - Filterbanks   (pdf, it, 5634 KB, 05/04/13)
•   L5 - 2D DWT and beyond   (pdf, it, 3748 KB, 12/04/13)
•   L5b - Hints on advanced concepts   (pdf, it, 2575 KB, 11/04/13)
•   L6 - Lifting steps   (pdf, it, 3413 KB, 19/04/13)
•   L7 - Hints on applications   (pdf, it, 3528 KB, 14/04/13)
•   L8 - Compression and Coding   (pdf, it, 2582 KB, 22/04/13)
•   Lab. session 1   (pdf, it, 4 KB, 11/03/13)
•   Lab. session 2   (zip, it, 2545 KB, 17/03/13)
•   Lab. session 3   (docx, it, 74 KB, 25/03/13)
•   Lab. Session 5   (zip, it, 897 KB, 08/04/13)
•   Lab. Session 6   (zip, it, 112 KB, 15/04/13)
•   Lab. Session 7   (zip, it, 352 KB, 22/04/13)
•   L - Int - 1 - Signals and Systems   (pdf, it, 2711 KB, 14/03/13)
•   L - Int - 2 - Fourier Transform   (pdf, it, 6094 KB, 27/03/13)
•   L - Int - 3 - 2D DFT   (pdf, it, 3019 KB, 27/03/13)