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Grenoble INP - UGA
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Informatique et Mathématiques appliquées
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Differential Calculus, Wavelets and Applications - WMM9AM50

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  • Number of hours

    • Lectures : 36.0
    • Tutorials : -
    • Laboratory works : -
    • Projects : -
    • Internship : -
    • Written tests : -
    ECTS : 6.0
  • Officials : Sylvain MEIGNEN

Goals

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, …).

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.

Prerequisites

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

Tests

Practical project (using MATLAB/WaveLab) .

The exam is given in english only FR

Calendar

The course exists in the following branches:

  • Curriculum - Master in Applied Mathematics - Semester 9 (this course is given in english only EN)
see the course schedule for 2022-2023

Additional Information

Course ID : WMM9AM50
Course language(s): FR

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 September 21, 2022

Université Grenoble Alpes