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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Phase retrieval and phaseless inverse scattering w
ith background information - Roman Novikov (CNRS &
amp\; Ă‰cole polytechnique)
DTSTART;TZID=Europe/London:20230516T090000
DTEND;TZID=Europe/London:20230516T100000
UID:TALK198094AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198094
DESCRIPTION:We consider the problem of finding a compactly sup
ported potential in the multidimensional Schrö
\;dinger equation from its differential scattering
cross section (squared modulus of the scattering
amplitude) at fixed energy. In the Born approximat
ion 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 phase information w
e use the method of a priori known background scat
terers. In particular\, we propose an iterative sc
heme for finding the potential from measurements o
f a single differential scattering cross section c
orresponding to the sum of the unknown potential a
nd a known background potential\, which is suffici
ently disjoint. The performance of the proposed al
gorithms is demonstrated in numerical examples.\nT
his talk is based on the work \; Hohage\, Novi
kov\, Sivkin\, Preprint 2022\, hal-03806616\n
\;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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