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Informatique et Mathématiques appliquées
Une voie, plusieurs choix

> Formation > Cursus ingénieur

Wavelets and applications - 5MM2531G

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  • Number of hours

    • Lectures : 18.0
    • Tutorials : -
    • Laboratory works : -
    • Projects : -
    • Internship : -
    • Written tests : -
    ECTS : 1.5
  • Officials : Kevin POLISANO

Goals

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.

Content

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, ...).

Prerequisites

  • Hilbert bases, Fourier transform (Applied Analysis)
  • Image Processing

Tests

Practical project (using MATLAB/WaveLab) .

N1=P(projet+soutenance)
N2=P

The exam is given in english only FR

Calendar

The course exists in the following branches:

  • Curriculum - Math. Modelling, Image & Simulation - Semester 9 (this course is given in english only EN)
  • Curriculum - Math. Modelling, Image & Simulation - Semester 9 (this course is given in english only EN)
  • Curriculum - Math. Modelling, Image & Simulation - Semester 9 (this course is given in english only EN)
see the course schedule for 2020-2021

Additional Information

Course ID : 5MM2531G
Course language(s): FR

The course is attached to the following structures:

You can find this course among all other courses.

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.

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Date of update January 15, 2017

French
Grenoble INP - Ensimag
École nationale supérieure d'informatique et de mathématiques appliquées
681, rue de la passerelle - Domaine universitaire - BP 72
38402 SAINT MARTIN D'HERES
 
 
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    Université Grenoble Alpes