Analysis and Mathematical Physics

, Volume 4, Issue 3, pp 199–220 | Cite as

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

Article

Abstract

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

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IdahoMoscowUSA

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