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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Microlocal properties of novel Ellipsoidal and hyp
erbolic Radon transforms - Todd Quinto (Tufts Univ
ersity)
DTSTART;TZID=Europe/London:20230516T133000
DTEND;TZID=Europe/London:20230516T143000
UID:TALK198103AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198103
DESCRIPTION:We present novel microlocal results for generalize
d ellipsoid and hyperboloid Radon transforms with
centers on surfaces in Euclidean Space\, and we ap
ply our results to Ultrasound Reflection Tomograph
y (URT). We introduce a new Radon transform\, $R$\
, which integrates compactly supported distributio
ns over ellipsoids and hyperboloids with centers o
n a smooth surface\, $S$. $R$ is shown to be a Fou
rier Integral Operator (FIO) and in our main theor
em we prove that $R$ satisfies the Bolker conditio
n if and only if the support of the function is in
a connected set that is not intersected by any pl
ane tangent to $S$ In this case\, backprojection t
ype reconstruction operators such as the normal op
erator $R^* R$ do not add artifacts to the reconst
ruction. We apply our results to a cylindrical geo
metry that could be used in URT. We investigate th
e visible singularities in this modality. In addit
ion\, we present reconstructions of image phantoms
in two dimensions that illustrate our microlocal
theory.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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