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Theses

Methodes multiresolutions non-lineaires. Applications au traitement d'image

Abstract : THIS THESIS INTRODUCE A CLASS OF BIDIMENSIONAL MULTIRESOLUTION TRANSFORMS WHICH DIFFER FROM STANDARD WAVELET DECOMPOSITIONS IN THE SENSE THAT THEY ARE BASED ON DATA DEPENDENT NONLINEAR OPERATORS. THESE OPERATORS ARE INSPIRED FROM THE ENO INTERPOLATION OPERATORS INTRODUCED BY HARTEN AND OSHER IN THE CONTEXT OF NUMERICAL SHOCK COMPUTATIONS. THE GOAL OF THE NONLINEAR PROCESSING IS TO PERFORM WITHIN THE TRANSFORM A SPECIFIC TREATEMENT OF EDGES WHICH WILL TAKE ADVANTAGE OF THEIR GEOMETRIC SMOOTHNESS IN ORDER TO OBTAIN SPARSER REPRESENTATIONS AND THEREFORE BETTER APPROXIMATIONS. WE SHALL ADRESSES THE NEW THEORETICAL DIFFICULTIES WHICH OCCUR WHEN ANALYZING THESE METHODS. WE PROVE THAT THEY YIELD THE SAME SMOOTHNESS CHARACTERIZATION FOR HÖLDER AND BESOV CLASSES, AS IN THE WAVELET CASE, AND WE PROVE THE STABILITY OF THESE REPRESENTATIONS, A KEY ISSUE IN THEIR APPLICATION TO DESIGN ADAPTIVE DATA COMPRESSION ALGORITHMS. WE PRESENT THEIR PRACTICAL PERFORMANCES FOR COMPRESSION AND DENOISING ON SYNTHETIC AND REAL IMAGES.
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https://tel.archives-ouvertes.fr/tel-00002016
Contributor : Basarab Matei <>
Submitted on : Tuesday, November 26, 2002 - 3:34:26 PM
Last modification on : Friday, May 29, 2020 - 4:01:47 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:39:12 PM

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  • HAL Id : tel-00002016, version 1

Citation

Basarab Matei. Methodes multiresolutions non-lineaires. Applications au traitement d'image. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2002. Français. ⟨tel-00002016⟩

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