Number of hours
- Lectures 18.0
- Projects -
- Tutorials -
- Internship -
- Laboratory works -
- Written tests -
ECTS
ECTS 1.5
Goal(s)
Wavelets are functions which are currently used in many fields : signal and image processing, numerical schemes for partial differential equations, scientific visualization.
The aim of the course is the construction and the study of the different wavelet bases, their applications to image processing (compression in JPEG2000 format, denoising, watermarking, ...) and to graph analysis (signal filtering and sampling on graphs, multi-scale community detection, ...).
Some practical works are devoted to applications in image processing and graph analysis, in order to prepare for the final project.
Responsible(s)
Kevin POLISANO
Content(s)
1) From Fourier to wavelets : the continuous wavelet transform, time-frequency representation.
2) Construction of wavelet bases : multiresolution analyses, fast algorithms (FWT), compactly supported wavelets.
3) Applications to image processing (edge detection, compression, denoising, watermarking, ...) and to graph analysis (signal filtering and sampling on graphs, multi-scale community detection, ...).
- Hilbert bases, Fourier transform (Applied Analysis)
- Image Processing
Test
Practical project (using MATLAB/WaveLab) .
N1=P(projet+soutenance)
N2=P
The exam is given in english only 
Calendar
The course exists in the following branches:
- Curriculum - Math. Modelling, Image & Simulation - Semester 9 (this course is given in english only
) - Curriculum - Math. Modelling, Image & Simulation - Semester 9 (this course is given in english only )
- Curriculum - Math. Modelling, Image & Simulation - Semester 9 (this course is given in english only )
Additional Information
Course ID : 5MM2531G
Course language(s):
The course is attached to the following structures:
You can find this course among all other courses.
Bibliography
S. MALLAT, A wavelet tour of signal processing, Academic Press, 1999.
Wavelet and Statistics, A. Antoniadis and G. Oppenheim eds, Springer, 1995.
B. TORRESANI, Analyse continue par ondelettes, Savoirs actuels - interéditions/CNRS éditions, 1995.