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.
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, ...).
Practical project (using MATLAB/WaveLab) .
The exam is given in english only
The course exists in the following branches:
Course ID : 5MM2531G
The course is attached to the following structures:
You can find this course among all other courses.
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.
Date of update January 15, 2017