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Informatique et Mathématiques appliquées
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> Formation > Cursus ingénieur

Wavelets & applications - WMM9AM15

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  • Number of hours

    • Lectures : 18.0
    ECTS : 3.0

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, …).

Contact Valérie PERRIER

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

Semester 9 - The exam is given in english only 

Practical project (using MATLAB/WaveLab) .



Additional Information

Semester 9 - This course is given in english only EN

Curriculum->Master 2 in Applied Mathematics->Semester 9

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

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes