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SUMMARY:Microlocal properties of novel Ellipsoidal and hyperbolic Radon tr
 ansforms - Todd Quinto (Tufts University)
DTSTART:20230516T123000Z
DTEND:20230516T133000Z
UID:TALK198103@talks.cam.ac.uk
DESCRIPTION:We present novel microlocal results for generalized ellipsoid 
 and hyperboloid Radon transforms with centers on surfaces in Euclidean Spa
 ce\, and we apply our results to Ultrasound Reflection Tomography (URT). W
 e introduce a new Radon transform\, $R$\, which integrates compactly suppo
 rted distributions over ellipsoids and hyperboloids with centers on a smoo
 th surface\, $S$. $R$ is shown to be a Fourier Integral Operator (FIO) and
  in our main theorem we prove that $R$ satisfies the Bolker condition if a
 nd only if the support of the function is in a connected set that is not i
 ntersected by any plane tangent to $S$ In this case\, backprojection type 
 reconstruction operators such as the normal operator $R^* R$ do not add ar
 tifacts to the reconstruction. We apply our results to a cylindrical geome
 try that could be used in URT. We investigate the visible singularities in
  this modality. In addition\, we present reconstructions of image phantoms
  in two dimensions that illustrate our microlocal theory.
LOCATION:Seminar Room 1\, Newton Institute
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