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The Factorization Method for Inverse Problems I
http://sms.cam.ac.uk/media/1159502
Kirsch, A (KIT)
Wednesday 27 July 2011, 09:0009:45
40
The Factorization Method for Inverse Problems I
http://sms.cam.ac.uk/media/1159502
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The Factorization Method for Inverse Problems I
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http://sms.cam.ac.uk/media/1159502
The Factorization Method for Inverse Problems I
Kirsch, A (KIT)
Wednesday 27 July 2011, 09:0009:45
Wed, 27 Jul 2011 14:38:20 +0100
Steve Greenham
Kirsch, A
Isaac Newton Institute
Kirsch, A
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Kirsch, A (KIT)
Wednesday 27 July 2011, 09:0009:45
Kirsch, A (KIT)
Wednesday 27 July 2011, 09:0009:45
Cambridge University
2633
http://sms.cam.ac.uk/media/1159502
The Factorization Method for Inverse Problems I
Kirsch, A (KIT)
Wednesday 27 July 2011, 09:0009:45
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 timeharmonic 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.
Steve Greenham
http://sms.cam.ac.uk/person/sg438
20110727T14:38:29+01:00
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