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SUMMARY:C3 - The Factorization Method for Inverse Problems IV - Kirsch\, A
  (KIT)
DTSTART:20110728T100000Z
DTEND:20110728T104500Z
UID:TALK32168@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk we introduce the Factorization Method for solving
  certain inverse problems. We will mainly consider inverse scattering prob
 lems but indicate the applicability of this method to other types of inver
 se problems at the end of the course. First\, we explain the Factorization
  Method for a simple finite dimensional example of an inverse scattering p
 roblem (scattering by point sources). Then we turn to a scattering problem
  for time-harmonic acoustic waves where plane waves are scattered by an in
 homogeneous medium. We will briefly discuss the direct problem with respec
 t to uniqueness and existence and derive the Born approximation. In the in
 verse scattering problem one tries to determine the index of refraction fr
 om the knowledge of the far field patterns. \nFirst we consider the Born a
 pproximation which linearizes the inverse problem. We apply\nthe Factoriza
 tion Method to this approximation for the determination of the support of 
 the\nrefractive contrast before we\, finally\, investigate this method for
  the full nonlinear problem. \nThis talk will be rather elementary. Knowle
 dge of some basic facts on Hilbert spaces (including the space L2(D) and t
 he notion of compactness) is sufficient for understanding this talk. \n
LOCATION:Seminar Room 1\, Newton Institute
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