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
- Wavelet-based coding
4) Wavelets in biomedicine
The exam consists in an oral examination aiming at verifying the comprehension of the theoretical aspects and includes theorems and demonstrations. The evaluation of the lab. activity is through the analysis of the activities performed during the year.