Inverting Spherical Radon Transform by a Closed-form Formula: A Microlocal Analytic Point of View

Abstract

Let $\mR$ be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface $\mS$. We study the inversion of $\mR$ by a closed-form formula. We approach the problem by studying an oscillatory integral, which depends on the observation surface $\mS$ as a parameter. We then derive various microlocal analytic properties of the associated closed-form inversion formula.

References in corpus (2)

• Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
• Inverting the spherical Radon transform for physically meaningful functions