C3 - The Factorization Method for Inverse Problems III
Seminar Room 1, Newton Institute
In this talk we introduce the Factorization Method for solving certain inverse problems. We will mainly consider inverse scattering problems but indicate the applicability of this method to other types of inverse problems at the end of the course. First, we explain the Factorization Method for a simple finite dimensional example of an inverse scattering problem (scattering by point sources). Then we turn to a scattering problem for time-harmonic acoustic waves where plane waves are scattered by an inhomogeneous medium. We will briefly discuss the direct problem with respect to uniqueness and existence and derive the Born approximation. In the inverse scattering problem one tries to determine the index of refraction from the knowledge of the far field patterns.
First we consider the Born approximation which linearizes the inverse problem. We apply the Factorization Method to this approximation for the determination of the support of the refractive contrast before we, finally, investigate this method for the full nonlinear problem.
This talk will be rather elementary. Knowledge of some basic facts on Hilbert spaces (including the space L2(D) and the notion of compactness) is sufficient for understanding this talk.
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