Mini-Symposia et Posters > Mini-Symposium 4: Inverse problems and shape optimization

The aim of this mini-symposium is to give a new ideas for the theoretical and numerical study of some inverse
and optimization problems. More precisely:
1. Numerical methods for the resolution of a shape optimization problem in a diffuse optical tomography(DOT) problem are introduced and discussed.
2. A novel idea based on the monotonicity of the Neumann-to-Dirichlet operator and the existence of localized potentials is presented to prove a conditional Lipschitz stabilty for the inverse problem of recovering Lamé parameters.
3. Reduced order model based on the Ritz decomposition is used to solve numerically a Cauchy problem.
4. Shape-based models for finding the best interpolation data in the compression of images with noise is introduced and discussed.

List of speakers

1. Rabeb Dhif, University of Tunis El Manar, National Engineering School of Tunis
Level-set based shape optimization approach for the inverse optical tomography problem.

2. Taher Rezgui, University of Tunis El Manar, National Engineering School of Tunis
Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity.

3. Mohamed Larbi, University of Tunis El Manar, National Engineering School of Tunis
Resolution of the Cauchy problem and uncertainty quantification via the Steklov-Poincaré approach.

4. Thomas Jacumin, University of  Haute-Alsace,
Optimal interpolation data for PDE-based compression of images with noise.