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/or shape and topological optimization problems in connection with acoustics, electromagnetism, elastodynamics, and waves in general.
Sought practical applications include radar and sonar applications, bio-medical imaging techniques, non-destructive testing, structural design, composite materials, ...
Roughly speaking, the model problem consists in determining information on, or optimizing the geometry (topology) and/or the physical properties of unknown targets from given constraints or measurements, for instance measurements of diffracted waves. 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.

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 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

  • DGA, CEA, Onera, Total, Cerfacs
  • Universities of Delaware (USA), Goettingen (Germany), ENIT (Tunisia), ITU (Turkey), Genova (Italy).

Research teams of the same theme :

Inria Headquarters and research centres

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