Volumes horaires
- CM 18.0
Crédits ECTS
Crédits ECTS 3.0
Objectif(s)
Wavelets are basis functions widely used in a large variety of fields: signal and image processing, numerical schemes for partial differential equations, scientific visualization. This course will present the construction and practical use of the wavelet transform, and their applications to image processing : Continuous wavelet transform, Fast Wavelet Transform (FWT), compression (JPEG2000 format), denoising, inverse problems. The theory will be illustrated by several applications in medical imaging (segmentation, local tomography, …).
Contact Valérie PERRIERContenu(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.
Prérequis
- Hilbert bases, Fourier transform (Applied Analysis)
- Image Processing
L'examen existe uniquement en anglais
Practical project (using MATLAB/WaveLab) .
N1=P(projet+soutenance)
N2=P
Le cours est donné uniquement en anglais
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.