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SUMMARY:Weighted Radon transforms of vector fields\, with applications to 
 magnetoacoustoelectric tomography - Leonid Kunyansky (University of Arizon
 a)
DTSTART:20230518T133000Z
DTEND:20230518T143000Z
UID:TALK198133@talks.cam.ac.uk
DESCRIPTION:Currently\, theory of ray transforms of vector and tensor fiel
 ds is well developed\, but the Radon transforms of such fields have not be
 en fully analyzed. We thus consider linearly weighted and unweighted longi
 tudinal and transversal Radon transforms of vector fields. As usual\, we u
 se the standard Helmholtz decomposition of smooth and fast decreasing vect
 or fields over the whole space. We show that such a decomposition produces
  potential and solenoidal components decreasing at infinity fast enough to
  guarantee the existence of the unweighted longitudinal and transversal Ra
 don transforms of these components.\nIt is known that reconstruction of an
  arbitrary vector field from only longitudinal or only transversal transfo
 rms is impossible. However\, for the cases when both linearly weighted and
  unweighted transforms of either one of the types are known\, we derive ex
 plicit inversion formulas for the full reconstruction of the field. Our in
 terest in the inversion of such transforms stems from a certain inverse pr
 oblem arising in magnetoacoustoelectric tomography (MAET). We will discuss
  the connection between the weighted Radon transforms and MAET\, and will 
 demonstrate performance of the new inversion formulas in numerical simulat
 ions.
LOCATION:Seminar Room 1\, Newton Institute
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