|Monday||11:30 AM - 1:30 PM||lesson||Lecture Hall G|
|Tuesday||10:30 AM - 1:30 PM||laboratorio||Laboratory Alfa|
|Wednesday||4:30 PM - 6:30 PM||lesson||Lecture Hall G|
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.
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. Classical paper-form exercises could also be performed.
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
3) Advanced coding systems
- Entropy, information, entropy coding
- Wavelet-based coding
4) Wavelets in biomedicine
|Stephane Mallat||A Wavelet Tour of Signal Processing (Edizione 2)||Academic Press||1999||9780124666061||The electronic version is also available eBook ISBN: 9780080520834|
Oral exam in 4 sessions. The exams are scheduled as follows: 1 exam in the Extraordinary Session at the end of the course, 1 exam in the Summer Session and 1 exams in the Fall Session. Each exam is split into two parts for the theory and laboratory parts, respectively, which can be passed separately and the whole evaluation is obtained as the mathematical average of the two evaluations. The exam is passed if each evaluation is greater or equal to 18/30. Each evaluation remains valid for the whole current academic year.
The aim of the written exam consists in verifying the comprehension of course contents and the capability to apply these contents for generalizing case studies presented during the course and for facing new issues. This comprehension may be verified also by asking theorems and proofs.
The aim of the laboratory exam is to verify the acquisition of the tools and methods and to assess the ability to apply such knowledge to the solution of new problems.