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SUMMARY:Phase retrieval and phaseless inverse scattering with background i
 nformation - Roman Novikov (CNRS &amp\; École polytechnique)
DTSTART:20230516T080000Z
DTEND:20230516T090000Z
UID:TALK198094@talks.cam.ac.uk
DESCRIPTION:We consider the problem of finding a compactly supported poten
 tial in the multidimensional Schr&ouml\;dinger equation from its different
 ial scattering cross section (squared modulus of the scattering amplitude)
  at fixed energy. In the Born approximation this problem simplifies to the
  phase retrieval problem of reconstructing the potential from the absolute
  value of its Fourier transform on a ball. To compensate for the missing p
 hase information we use the method of a priori known background scatterers
 . In particular\, we propose an iterative scheme for finding the potential
  from measurements of a single differential scattering cross section corre
 sponding to the sum of the unknown potential and a known background potent
 ial\, which is sufficiently disjoint. The performance of the proposed algo
 rithms is demonstrated in numerical examples.\nThis talk is based on the w
 ork&nbsp\; Hohage\, Novikov\, Sivkin\, Preprint 2022\, hal-03806616\n&nbsp
 \;
LOCATION:Seminar Room 1\, Newton Institute
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