Ensimag Rubrique Formation 2022

Wavelets and applications - WMMS533V

  • 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 PERRIER

Contenu(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

Contrôle des connaissances

L'examen existe uniquement en anglais 

Practical project (using MATLAB/WaveLab) .



N1=P(projet+soutenance)
N2=P

Informations complémentaires

Le cours est donné uniquement en anglais EN

Cursus ingénieur->MSIAM->MSIAM - Semester 3

Bibliographie

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.