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.
Analysis and Mathematical Physics – Springer Journals
Published: Sep 11, 2013