Multiresolution analysis: theory and applications (2014/2015)

Course code
4S001407
Name of lecturer
Gloria Menegaz
Coordinator
Gloria Menegaz
Number of ECTS credits allocated
6
Other available courses
Academic sector
ING-INF/05 - INFORMATION PROCESSING SYSTEMS
Language of instruction
Italian
Period
II sem. dal Mar 2, 2015 al Jun 12, 2015.

Lesson timetable

II sem.
Day Time Type Place Note
Monday 11:30 AM - 1:30 PM lesson Lecture Hall G  
Tuesday 8:30 AM - 10:30 AM lesson Lecture Hall I  
Wednesday 2:30 PM - 5:30 PM laboratorio Laboratory Gamma  

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

Syllabus

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

Assessment methods and criteria

Theory: oral or written

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 aids

Documents