Waves and imaging:

Concepts, Theory and Applications

Program (slides)

1. Basic materials to study of scattering problems at fixed frequency (Radiation Condition, Fredholm theory, The Rellich lemma and unique continuation principle).


2. 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


3. Uniqueness in the framework of geometrical optic solutions.


4. Presentation and analysis of some nonlinear inversion algorithms (Landweber and Gauss-Newton).


5. 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)