FRACTALES, ONDELETTES ET IMAGERIE MEDICALE

Jacques LEVY VEHEL

INRIA (Rocquencourt), France

Le rcm2 organise un atelier et une conference donnes par

J. Levy Vehel, les jeudi 11 Avril et vendredi 12 avril

2002. L’atelier portera sur l’analyse multifractale des

signaux avec des demonstrations sous Matlab. Le seminaire

fera etat des plus recents travaux du conferencier dans le

domaine de l’estimation de signaux 2d.

ATTENTION : POUR L’ATELIER DU 11 AVRIL, PRIERE DE S’INSCRIRE

AUPRES DE FAHIMA NEKKA (fahima.nekka@umontreal.ca)

(LE NOMBRE DE PLACE EST LIMITE A 20)

JEUDI 11 AVRIL

9h00-11h30 et 13h30-16h00

Local : 5197

Pavillon Andre-Aisenstadt

Universite de Montreal

«Multifractal Analysis of Signals and Images»

This tutorial will present the basic concepts of fractal

and multifractal analysis in view of their application to

signal and image processing. The course will adress both

theoretical developments and real-world applications, with

an emphasis on practical experiments that will be performed

using the software toolbox FracLab.

1- Global measures of regularity

- Recalls on the box and Hausdorff dimensions

- The regularization dimension

- Application to classification

2- Local measures of regularity

- Pointwise Holder exponent

- Local Holder exponent

- 2-microlocal analysis

- Pratical estimation of the regularity exponents

- Application to signal and image denoising

- Application to change detection.

3- Multifractal analysis

- Haussdorff spectrum

- Large Deviation spectrum

- Legendre spectrum

- Practical estimation of the multifractal spectra

- Application to image segmentation

4- Numerical experiments with FracLab

- Synthesis of fractal signals

- Estimation of the regularisation dimension

- Image denoising

- Image segmentation

VENDREDI 12 AVRIL

10h00-11h00

Local : 6214

Pavillon Andre-Aisenstadt

Universite de Montreal

«Multifractal Image Denoising»

Multifractal based denoising has been developped to deal

with the situation where one needs to recover an irregular

underlying signal corrupted with non necessarily additive

white Gaussian noise. This often happens in practice, for

instance in synthetic aperture radar imaging or echography:

In such cases, the noise is non Gaussian and has complex

non linear interaction with the data. In addition, the

underlying signal is itself irregular, with essential

infomation contained in the regularity structure. Thus any

technique that would oversmooth the data would lead to

unacceptable loss for further processing (e.g. detection).

Multifractal denoising is a regularization technique that

imposes a local constraint on the reconstructed signal:

Instead of requiring that the denoised signal belongs to

some global smoothness class, one seeks a regularized signal

with prescribed Holder exponent. We shall developp the

underlying theoretical concepts and explain ion details the

implementation of this technique. Results on SAR and medical

images will be shown.

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Muriel Pasqualetti

Rcm2 et Centre de recherches mathématiques

Tél. 343 75 01