UE Wavelets and applications

Degrees incorporating this pedagocial element :

Description

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, …).

Contents :

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.

Evaluation :

Practical project (using MATLAB/WaveLab) + defence: P

The final mark is obtained as follows (sessions 1 and 2) : P

Prerequisites

Hilbert bases, Fourier transform (Applied Analysis)

Image Processing

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.