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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Weighted Radon transforms of vector fields\, with
applications to magnetoacoustoelectric tomography
- Leonid Kunyansky (University of Arizona)
DTSTART;TZID=Europe/London:20230518T143000
DTEND;TZID=Europe/London:20230518T153000
UID:TALK198133AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198133
DESCRIPTION:Currently\, theory of ray transforms of vector and
tensor fields is well developed\, but the Radon t
ransforms of such fields have not been fully analy
zed. We thus consider linearly weighted and unweig
hted longitudinal and transversal Radon transforms
of vector fields. As usual\, we use the standard
Helmholtz decomposition of smooth and fast decreas
ing vector fields over the whole space. We show th
at such a decomposition produces potential and sol
enoidal components decreasing at infinity fast eno
ugh to guarantee the existence of the unweighted l
ongitudinal and transversal Radon transforms of th
ese components.\nIt is known that reconstruction o
f an arbitrary vector field from only longitudinal
or only transversal transforms is impossible. How
ever\, for the cases when both linearly weighted a
nd unweighted transforms of either one of the type
s are known\, we derive explicit inversion formula
s for the full reconstruction of the field. Our in
terest in the inversion of such transforms stems f
rom a certain inverse problem arising in magnetoac
oustoelectric tomography (MAET). We will discuss t
he connection between the weighted Radon transform
s and MAET\, and will demonstrate performance of t
he new inversion formulas in numerical simulations
.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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