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On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view

On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view Let $$\mathcal R $$ R be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface $$\mathcal S $$ S . We study the construction of a function $$f$$ f from $$\mathcal R (f)$$ R ( f ) by a closed-form formula. We approach the problem by studying an oscillatory integral, which depends on the observation surface $$\mathcal S $$ S as a parameter. We then derive various microlocal analytic properties of the associated closed-form reconstruction formula. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view

Analysis and Mathematical Physics , Volume 4 (3) – Sep 11, 2013

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Springer Basel
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-013-0063-8
Publisher site
See Article on Publisher Site

Abstract

Let $$\mathcal R $$ R be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface $$\mathcal S $$ S . We study the construction of a function $$f$$ f from $$\mathcal R (f)$$ R ( f ) by a closed-form formula. We approach the problem by studying an oscillatory integral, which depends on the observation surface $$\mathcal S $$ S as a parameter. We then derive various microlocal analytic properties of the associated closed-form reconstruction formula.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Sep 11, 2013

References