Teaching code

4S003737

Teacher

Gloria Menegaz

Coordinatore

Gloria Menegaz

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

INF/01 - INFORMATICS

Period

I sem. dal Oct 3, 2016 al Jan 31, 2017.

Moodle Seminars

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. Classical paper-form exercises could also be performed.

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

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.

Teaching materials

•   C1 - Signals&Systems   (pdf, en, 2769 KB, 10/10/16)
•   C2 - Fourier Transform   (pdf, en, 5861 KB, 19/10/16)
•   C3 - Fourier Transform in 2D   (pdf, en, 3022 KB, 10/10/16)
•   Esercitazione 1   (msword, en, 27 KB, 10/10/16)
•   Esercitazione 2   (zip, it, 53 KB, 18/10/16)
•   Esercitazione 5   (zip, it, 797 KB, 21/11/16)
•   Esercitazione 6   (msword, it, 81 KB, 29/11/16)
•   Esercitazione 7 - LSQ   (zip, it, 137 KB, 10/12/16)
•   Esercitazione 8   (zip, it, 23747 KB, 12/12/16)
•   L1 - Introduction   (vnd.ms-powerpoint, en, 26898 KB, 10/10/16)
•   L2 - Multiresolution   (pdf, it, 3270 KB, 12/10/16)
•   L3 - Wavelet bases   (pdf, it, 8141 KB, 23/10/16)
•   L4 - Wavelets and Filterbanks   (pdf, it, 6230 KB, 09/11/16)
•   L5 - Bidimensional WT   (pdf, it, 3186 KB, 15/11/16)
•   L6 - Coding principles   (pdf, it, 2617 KB, 21/11/16)
•   L7-JPEG2000   (pdf, it, 2029 KB, 10/12/16)
•   L8-AdvancedConcepts   (pdf, it, 2677 KB, 10/12/16)
•   L-LSQ-Applications   (pdf, it, 3838 KB, 10/12/16)
•   Papers-Coding   (zip, it, 4453 KB, 10/12/16)