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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:C3 - The Factorization Method for Inverse Problems
I - Kirsch\, A (KIT)
DTSTART;TZID=Europe/London:20110727T090000
DTEND;TZID=Europe/London:20110727T094500
UID:TALK32160AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32160
DESCRIPTION:In this talk we introduce the Factorization Method
for solving certain inverse problems. We will mai
nly consider inverse scattering problems but indic
ate the applicability of this method to other type
s of inverse problems at the end of the course. Fi
rst\, we explain the Factorization Method for a si
mple finite dimensional example of an inverse scat
tering 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 th
e inverse scattering problem one tries to determin
e the index of refraction from the knowledge of th
e far field patterns. \nFirst we consider the Born
approximation which linearizes the inverse proble
m. We apply\nthe Factorization Method to this appr
oximation for the determination of the support of
the\nrefractive contrast before we\, finally\, inv
estigate this method for the full nonlinear proble
m. \nThis talk will be rather elementary. Knowledg
e of some basic facts on Hilbert spaces (including
the space L2(D) and the notion of compactness) is
sufficient for understanding this talk. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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