Waves and imaging:
Concepts, Theory and Applications
Responsable : Houssem Haddar
- Basic materials to study of scattering problems at fixed frequency (Radiation Condition, Fredholm theory, The Rellich lemma and unique continuation principle).
- Discussion of some linearization approaches: Born approximation, Time reversal and Synthetic Aperture Radar principles
Notion of ill-posed problems and some rudiments on regularization theory
- Uniqueness in the framework of geometrical optic solutions.
- Presentation and analysis of some nonlinear inversion algorithms (Landweber and Gauss-Newton).
- Presentation and analysis of so-called sampling methods to solve the geometrical inverse problem (Linear Sampling Method, Factorization Method).
Course Notes (pdf)
Bibliography
- Inverse Scattering Theory and Transmission Eigenvalues
F. Cakoni, D. Colton and H. Haddar
(SIAM, 2016)
- Inverse Acoustic and Electromagnetic Scattering Theory,
D. Colton and R. Kress
(Springer, 2013)
- An Introduction to the Mathematical Theory of Inverse Problems, A. Kirsch
(Springer, 1996)
- An Introduction to the Mathematical Theory of Inverse Problems, A. Kirsch
(Springer, 1996)
- Regularization of Inverse Problems, H.W. Engl, M. Hanke and
A. Neubauer (Kluwer Academic Publisher, 2000)
-
The Factorization Method for Inverse Problems, A. Kirsch and N. Grinberg (OUP
Oxford, 2008)
Last modified: Thu Oct 25 12:05:27 CEST 2018