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 (JPEG2000 format) denoising, and watermarking.
Some practical works are devoted to applications in image processing, 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.
Practical project (using MATLAB/WaveLab) .
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.