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DEFI Research team

Shape reconstruction and identification

Team presentation

The research activity of our team is dedicated to the design, analysis and implementation
of efficient numerical methods to solve inverse and shape/topological optimization
problems in connection with acoustics, electromagnetism, elastodynamics, and
diffusion. Sought practical applications include radar and sonar applications,
bio-medical imaging techniques, non-destructive testing, structural design,
composite materials, and diffusion magnetic resonance imaging.

Roughly speaking, the model problem consists in determining information on,
or optimizing the geometry (topology) and the physical properties of unknown targets
from given constraints or measurements, for instance, measurements of diffracted waves
or induced magnetic fields. In general this kind of problems is non-linear. The inverse ones are also severely ill-posed and therefore require special attention from regularization point of view,
and non-trivial adaptations of classical optimization methods.
We are particularly interested in the development of fast methods that
are suited for real-time applications and/or large scale problems. These goals
require to work on both the physical and the mathematical models involved and
indeed a solid expertise in related numerical algorithms.

Our scientific research interests are three-fold:

  • Theoretical understanding and analysis of the forward and inverse mathematical models, including in particular the development of simplified models for adequate asymptotic configurations.
  • The design of efficient numerical optimization/inversion methods which are quick and robust with respect to noise. Special attention will be paid to algorithms capable of treating large scale problems (e.g. 3-D problems) and/or suited for real-time imaging.
  • Development of prototype/industrial softwares for precise applications or tutorial toolboxes.

Research themes

  • Non-iterative methods for inverse boundary value problems, inverse scattering problems and imaging (Samplings methods for multistatic data at a fixed frequency, Asymptotic methods, Qualitative estimates for target identification problems, ...)
  • Shape and topological optimization methods with application to inverse problems (Homogenization and small amplitude homogenization methods, Level Set methods, Toplogical gradient methods, ...)
  • Hybrid methods
  • Regularization and stability issues for ill-posed problems and imaging (Stability estimates, Methods of total variation, Edge preserving image reconstructions, ...)

International and industrial relations

  • EDF, DGA, Xenocs, ART-FI, Neurospin
  • Universities of Delaware (USA), Rutgers University (USA), University of Bremen (Germany), University of Goettingen (Germany), ENIT (Tunisia), ITU (Turkey), University of Genova (Italy).